Wordscapes(tm) and the Sense of Repeated Puzzles Mike Beeler January 2022 CONTENTS ARE PUZZLES REPEATED? 1. Introduction 2. Conclusion and getting started 3. If same means same letter set 4. If same means same accepted words 5. If same means mostly the same answer words 6. If same means same answer words 7. If same means same words and layout THE GAME AND ANALYSIS 8. Method and limitations 9. Wordscapes basics 10. Bonus words, 3-letter words, and wordscapescheat.com 11. Background images 12. Glossary CURIOSITIES 13. A tale of LARCH and TUPELO 14. No vortex in the layout 15. Sizes and stats 16. Multiple keyword candidates 17. How often specific answer words occur 18. Are daily puzzles repeats? TEDIOUS SUPPORTING DATA 19. List of nearly same answer word sets 20. List of levels with same answer word set 21. Keyword intersections for 49 pairs with same answer word set ----- ARE PUZZLES REPEATED? ----- 1. Introduction Wordscapes players sometimes feel the game repeats puzzles. Online comments, and my own experience, suggest that the same puzzle appeared before, at an earlier level. I wanted to analyze several Wordscapes puzzles (levels) to see how much repetition there is. This paper reports my results, and some observations and comments. I will dive right into that motivating question. Auxiliary subjects, such as discussion of what Wordscapes is, examples, counts of cases, is later. Jump to whatever section seems most interesting. I especially suggest the "Method and limitations" section. Tables and diagrams herein are most readable in monospace font. It's kind of long. I got curious about one thing after another, and enjoyed finding answers. It has everything but the kitchen sink. (SINK is an answer word in 5 puzzles, but KITCHEN in none!) Read as a buffet -- take what interests you and ignore the rest. While sparked by a serious question of whether repeat puzzles are real or imagined, this project was undertaken for fun, and this report is meant for fun. Wordscapes is a fun game, and its creators are to be congratulated. No disparaging effect is intended! All in good fun! ----- 2. Conclusion and getting started "Life is short; eat dessert first." So, here's the conclusion: There are exact repeats, but they are so rare that repetition of things other than full puzzles may explain why users feel they have seen puzzles repeated. We have to ask, what does "same" mean, when you feel you've seen the "same" puzzle before? We explore plausible meanings of "same", and what the analysis of many Wordscapes levels shows in relation to each version of "same". ----- 3. If same means same letter set Consider the letter set in the circle on the Wordscapes screen. Some players may feel that if the set of letters from which to make words is identical, then the puzzles are the same. After all, with the same set of letters, you can make the same words. The early levels, 1-80, have letter sets of 3, 4 or 5 letters. Among these levels, every letter set is unique; from level 1 (A C T) to level 80 (A E L R Y), all are unique. So let us turn to the later, mainstream, levels that have 6 or 7 letters. Among the mainstream levels 81-2580, there are 2092 different letter sets. 1726 letter sets appear once. 327 letter sets appear twice. 36 letter sets appear three times. 3 letter sets appear four times. This accounts for the 2500 levels. The letter sets that appear four times, and their levels, are: I N O O P S - levels 613, 674, 791, 1774 A C I S T T - levels 498, 582, 730, 1837 G L N S U Y - levels 339, 465, 562, 1918 (These are listed in increasing order of the last occurrence; remember that if this study included more levels, more repeats might be found.) For a user with a good memory, they might notice repeats of the second and subsequent occurrences. Thus they might notice 327 * 1 + 36 * 2 + 3 * 3 = 327 + 72 + 9 = 408 puzzles they had seen before, out of 2500 mainstream puzzles. That is about 1 in 6, or 16%. If identical letter sets is the criterion for puzzle sameness, the user would say there definitely are repeats. ----- 4. If same means same accepted words Another interpretation of "same puzzle" is that all the accepted words of one puzzle, are accepted for the other puzzle. On each puzzle, the words may be accepted as answer words or as bonus words. A player might remember whether a word was accepted at all, better than whether it went onto the puzzle layout or into the bonus word bank. I did not capture the bonus word list for most puzzles, so I cannot tell whether having the same letter set always means the accepted words are the same. However, in the few dozen puzzles I checked, that is true. One wrinkle arises if one puzzle allows 3-letter words, but the other does not. Then, the accepted word sets are nearly certain to be different. I leave it as a conjecture, that having the same letter set is equivalent to having the same accepted words, except for blocking of 3-letter words. If that's true, then "same accepted words" is equivalent to "same letter set", discussed above. ----- 5. If same means mostly the same answer words A user noticing answer words that seem to be the same words as in a previous puzzle, may understandably suspect that the puzzle is a duplicate. But how similar must the word sets be? Is half the words being identical enough? Or two thirds, or three quarters? Rather than a fraction, how about a count of differences -- five words, or four words, or three words different? The criteria for two answer word sets being mostly the same, is a swamp, a rabbit hole. There are many plausible choices, and seemingly little insight to be gained by pursuing them. But, rather than giving up, let us make a simple, limited test at the edge of the swamp. Let us look for cases where the answer word sets of two puzzles differ by just one word. There are two ways this can occur: one set can be the same as another, but with one additional word; or, the sets can have the same number of words, but with one word in one set replaced by a different word in the other set. The formula for the number of pairs of n objects is n*(n-1)/2. For Wordscapes puzzles of level 1-2580, we have: 2580 * (2580 - 1) / 2 = 3326910 Analysis of these pairs finds: 3326844 pairs have difference greater than one word 52 pairs have one additional word in one puzzle 14 pairs have same word count but one word differs The vast majority of pairs have a greater difference than one word; they are farther out in the swamp. Only 66 pairs, 0.002%, about 1 in 50400 pairs, differ by one word. This is so small a fraction that it seems unlikely it explains the sense of repeated puzzles. Perhaps the impression comes from other things, explored in sections below. Or from word sets that differ by two words, or three, or... oops! Sounds like a swamp! Before we leave this meaning of "same", note one curious fact. The puzzles in the 66 cases do not seem to be randomly distributed among the 2580 levels analyzed. Suppose we list the 132 levels (2 in each of 66 pairs), sort them, and take the difference between adjacent entries. This gives us 131 gaps between levels that appear in the 66 pairs. The average gap is roughly 2580/132, or about 20. But the actual gaps do not fall around 20; most gaps are smaller. There are 90 gaps of 1 to 19, the lion's share of the 131 gaps. 3 gaps are exactly 20, and only 38 gaps are 21 to the largest. (That largest gap is 119 between levels; or 121 before the first; or 144 after the last). This suggests that the puzzles that occur in pairs whose answer word sets differ by one word, appear in clusters, not randomly spaced. Perhaps the puzzle makers used some selection process that results in these clusters. ----- 6. If same means same answer words Suppose we consider puzzles to be the same only if the same words are answer words in both puzzles. Bonus words are excluded; only the set of answer words matters. Among the early puzzles, levels 1-80, there are no duplicate answer word sets. So turn to the mainstream puzzles, levels 81-2580. Here, there are 2451 different answer word sets. 2402 answer word sets appear once. 49 answer word sets appear twice. This accounts for the 2500 levels. A later section lists the 49 puzzle pairs that share an answer word set. In my opinion, 49 puzzles, while only about 2% of the 2500 mainstream levels 81-2580, is enough to convince some users they have seen the puzzle before. Here again, as with the pairs with answer word sets differing by just one word, there seems to be some clustering of the puzzles. In these 49 pairs, consider the difference in level number between the earlier puzzle and the later puzzle. In 41 pairs, that is more than 1000 levels. And in another 5, it is more than 160. But in 3 cases, it is under 100: levels 654 and 673, difference = 19 levels 527 and 573, difference = 46 levels 498 and 582, difference = 84 These, especially the pair only 19 apart, might be played so near in time that the user could sense that they had seen the same answer words before, and conclude that puzzles were repeated. The second puzzles in these three pairs are within only 100 of each other (573 to 673), enhancing the chance that the user would sense repetition. ----- 7. If same means same words and layout To me, none of the criteria considered so far are enough to say two Wordscapes puzzles are the same. Only puzzles with the same layout, the positions of the words on the criss-cross grid, suffices. Because the intersections with other words are often a huge hint! I can blast away at populating many of the words that the letter set makes. Once those appear in the layout, they become a great help in figuring out the intersecting words. So, let us explore whether Wordscapes repeats puzzles including their layout. We already eliminated most of the levels 1-2580, because with a different answer word set, puzzles cannot have words fall in the same place in the layout. So only the 49 pairs noted above need be considered. A simple way to show that a pair of these layouts cannot be identical is to list the words that some chosen word intersects. We choose the keyword, because it contains as many letters as possible, giving a good chance of intersecting several words. The intersected words are listed in the same order the keyword intersects them, from the first letter of the keyword to the last. For example, consider levels 527 and 573: . . . . . T O O . . L . . . T . . . . . . O . U . . O . L O O K . L O O K O U T T . O . O . O . . O . U . L . L O U T L O O K . L O O T . . . O O . . . K . . . . K . . . L . O L O T . O . . . . . . . T O O K . . O . U . . . . . . . . T . . . . O U T . . . level 527 level 573 These are clearly different, but it is nice to have a simple, textual statement that indicates their difference. We choose keyword LOOKOUT, and list the words it intersects, from the first L to the final T: 527 - LOOKOUT intersects LOOK, OUT, TOOL, OUTLOOK 573 - LOOKOUT intersects LOOK, OUTLOOK, OUT If the two lists differ in any word or in their order, the two layouts must be different. If the two lists are identical, there is no proof; the intersections can be at different positions on the keyword or on cross words. But this tool is often enough. In fact, of the 49 candidate puzzle pairs, the intersection list eliminates 42 pairs. Seven pairs require further investigation, because their intersection lists are the same. They are: 382 and 1893 - INNATE intersects ANTI, INANE 731 and 1935 - MAINLY intersects NAIL, LAY 786 and 1950 - SHUFFLE intersects SHELF, FLUE 871 and 1953 - HALLWAY intersects HALL, ALLAY, WALL 748 and 1972 - SHORTLY intersects SLOTH, STORY 987 and 2186 - DAGGER intersects DEAR, AGED 978 and 2216 - COWBELL intersects COWL, BOLL, BELLOW Another simple and easy tool is whether the puzzles have the same island word (a word by itself in the layout). This eliminates 3 of the pairs: 382 - island word NINE 1893 - no island word 748 - no island word 1972 - island word SHORT 987 - no island word 2186 - island word DARE This leaves 4 puzzle pairs. Examination finds that the puzzles in each pair are identical! The bonus words in each pair are also identical. So, in my book, these are truly repeated puzzles. Although rare, they answer our goal question with a resounding "Yes, Wordscapes does repeat puzzles." For easy reference, the details are shown below, including the Wordscapes name (group: pack and number) for each. 731 (Desert: Spire 11) and 1935 (Formation: Calm 15) - 11W x 11H answer words: AIL AIM ANY INLAY LAIN LAM LAY MAIL MAIN MAINLY MAN MANLY MAY MIL NAIL NAY NIL YAM YIN bonus words: AMYL LIMN MANY MYNA 3-letter words: accepted . . . A . . . . I . . . M . I . . L . N . . N A I L . M A I L . . . I . . . . I . A . . . N . . M A N L Y . . . L A Y . . . A . . . . Y . A I M . M A I N . . . M . A . . . . I . . . . A N Y . M I L . . . . . . I . A . . . . . . . . N A Y . . levels 731 & 1935 786 (Desert: Sand 2) and 1950 (Formation: Set 14) - 11W x 8H answer words: FLESH FLUE FLUSH FUEL FUSE HUES HUFF LUSH SELF SHELF SHUFFLE bonus words: FLUES FLUS FUELS HUFFS SHUL 3-letter words: rejected . . . . . . F L E S H . . . . . F . U . E . . . . . H U E S . L . . S . . . E . H U F F S H U F F L E . . . . . E . . L . . . . . . . L . . U . F L U S H . F U S E . . . . . . levels 786 & 1950 871 (Ocean: Depth 7) and 1953 (Formation: Serene 1) - 7W x 7H answer words: ALLAY ALLY AWAY HALL HALLWAY WALL bonus words: YAWL 3-letter words: rejected A W A Y . . . . . . . . . . . . . A . . . . H . L . W . H A L L W A Y . L . A . L . A L L Y . L . levels 871 & 1953 978 (Lake: Set 2) and 2216 (Marsh: Vivid 8) - 12W x 10H answer words: BELL BELLOW BELOW BLEW BLOW BOLL BOWL CELL CELLO COWBELL COWL ELBOW LOBE WELL bonus words: BLOC BOLE BOWEL LOWE 3-letter words: rejected . . . . B . C . . . . . . . B . E . E . . . . . . C E L L . L . . . . . . . L . O . L . . . . B . B L E W . O . . . . E . L . . . . . . . . . L B O W L . C O W B E L L . W . O . O . . O . . O . . . B . W . E L B O W . . W E L L . . L . . . levels 978 & 2216 ----- THE GAME AND ANALYSIS ----- 8. Method and limitations I needed to gather the answer word set for hundreds of puzzles. Manually transcribing them from Wordscapes games was impractical. Fortunately, there are internet sites that have solutions. I used wordscapescheat.com, which has the answer word set (and layout) for each puzzle. A simple copy and paste, per puzzle, was a bit tedious but workable. It is an easy to use, well designed site. (wordscapescheat.com is copyright by Firecracker Software, in no way associated with Peoplefun, the makers of Wordscapes.) I decided to limit the number of answer word sets I collected for my dataset. I chose to include the 80 early levels, and 2500 mainstream levels. My reasoning is that 2500 mainstream levels should be enough to detect repeats, if puzzles are repeated; 2500 is a good fraction of the puzzles before Wordscapes transitions to the "master" puzzles at level 6000; I solved 2580 puzzles when I decided to do an analysis; and, I simply got tired of gathering the data. So, all the results herein are qualified with "based on levels 1-2580". It seems that Wordscapes puzzles may be a slightly moving target. An online criticism of Wordscapes was its use of MONGOL as an answer word. While that is a correct word for a native of Mongolia, it has become tainted as a disparaging word for people with Down syndrome. Peoplefun said they would remove it from Wordscapes in a future release. The point here is that the game might change from time to time. I don't know what "version number" the Wordscapes games I looked at, or the answer sets in wordscapescheat.com, correspond to. Among the levels 1-2580 I looked at, none have a letter set that can spell MONGOL. (The incident was in January 2019.) Finally, American English has many arbitrary elements in spelling and in what is and is not a word. Even though I poke fun at some of the choices, it is the prerogative of a game maker to design the game, including spelling and word legality. Peoplefun has done an admirable job of building a fun game, including reasonable choices of words. ----- 9. Wordscapes basics Wordscapes is like a sparse crossword puzzle in which all words must be made from the letters shown in a circle. The letters are upper case only. Words that fall into spaces on the puzzle layout are called answer words. Words that the game recognizes but that do not fall into the layout are added to a bank of bonus words while the puzzle is being solved. The user can use hints of various types. Using a bullseye (target), you can specify which letter to reveal in the layout. The rocket reveals several letters at random. The light bulb reveals one letter at random. The re-order arrows scramble the order of the letters in the letter set circle; that helps when you are stuck trying to find a word. Game coins are earned by finding bonus words, and completing 16 puzzles. The coins can be used to get hints. Upon startup each day, the user may be given a choice of 3 boxes (rewards, gifts). The chosen box may yield a number of coins, a hint, or "spelling bees". The spelling bees reveal a few letters of the next puzzle. Puzzles are named in two ways. One is the level number, like a serial number for the puzzle. Levels start at 1 and increase by 1. The other name is a hirarchical system, like year, month, and day. The corresponding terms in Wordscapes are group, pack and number. In general, there are 16 numbers per pack, and 5 packs per group; thus, 80 puzzles per group. Groups have general names, such as Sunrise and Forest; packs have more detailed names, such as Rise, Grow and Shine within the Sunrise group. Within each pack, the individual puzzles have numbers, 1 to 16. The first 80 puzzles are simpler, helping the player learn how to play. They also have fewer puzzles per pack, and packs per group: The first group, Sunrise, has only 3 packs, each with only 4 puzzles: Sunrise: Rise 1-4 = levels 1-4 (4 levels) Sunrise: Grow 1-4 = levels 5-8 (4 levels) Sunrise: Shine 1-4 = levels 9-12 (4 levels) The second group, Forest, has the normal 5 packs, but only 68 puzzles: Forest: Pine 1-8 = levels 13-20 (8 levels) Forest: Dew 1-12 = levels 21-32 (12 levels) Forest: Flow 1-16 = levels 33-48 (16 levels) Forest: Fog 1-16 = levels 49-64 (16 levels) Forest: Life 1-16 = levels 65-80 (16 levels) From there on, each group has 5 packs, and each pack has 16 puzzles (levels). Pack names are occasionally reused. For example, Set is used in both of these: Lake: Set 1-16 = levels 977-992 Formation: Set 1-16 = levels 1937-1952 That scheme continues to level 6000, beyond which there are "master" levels. (I mostly use level numbers. When using the hierarchical system, I use "group: pack number", analogous to "year month day". Wordscapescheat.com seems to use "pack number: group", like "month day year". Beware.) The number of letters in the letter set grows as the level increases: Sunrise: Rise (4 levels) has 3 letters Sunrise: Grow and Shine (8 levels) have 4 letters Forest: Pine through Life (68 levels) have 5 letters After level 80, all puzzles have 6 or 7 letters. As far as I can tell, no level, even those after 6000, has more than 7 letters. Because the first 80 levels are introductory, I call them "early"; puzzles starting with level 81 I call "mainstream". In some analyses, I exclude the early puzzles to avoid skewing the conclusions. Within the mainstream puzzles, do 7-letter puzzles become more frequent? Yes. The first 7-letter puzzle occurs at level 483. By around level 800, 6-letter and 7-letter puzzles have become equally common, and they remain so. The table below shows the counts for each 100 mainstream puzzles. The first row gives the level number; if it is n, that column is for levels 100 * n - 19 through 100 * n + 80. (Example: column headed "1" is for levels 81 through 180.) Row 2 is the number of 6-letter puzzles among those 100 puzzles; "C" = 100. Row 3 is the number of 7-letter puzzles. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 C C C C 64 67 57 49 51 51 50 49 49 51 50 50 49 49 51 51 50 49 52 50 51 0 0 0 0 36 33 43 51 49 49 50 51 51 49 50 50 51 51 49 49 50 51 48 50 49 Every Wordscapes puzzle seems to have at least one answer word that uses all the letters in the letter set. (I call this, or the alphabetically first one if there are more than one, the "keyword".) It does not have to be so. For example, consider the first 6-letter puzzle (level 81): letter set: D E P T U Y answer words: DEPUTY DUPE DUTY DYE PET PUT TYPED YEP YET YUP Keyword DEPUTY is not needed to specify the letter set; just DYE and PUT suffice. For this project, I inferred the letter set from the answer words, because wordscapescheat.com does not have the letter set itself. So my program checks that at least one answer word uses all the letters implied by all the answer words. Some puzzles disallow 3-letter words, both as answer words and bonus words. This is discussed further in the section on bonus words. Peoplefun, the makers of Wordscapes, prunes their word list of "bad" words that may be offensive. This explains why SHIT is never an accepted word, either answer or bonus, even though 13 puzzles, levels 15, 280, ..., 2573, have letter sets containing the four needed letters. I suspect Peoplefun may also make a subtler distinction on some words, allowing them to be accepted as bonus words but never used as answer words. It seems that Peoplefun has a master dictionary for Wordscapes puzzles. That is, if a word is allowed in one puzzle, it seems to always be allowed in another puzzle (if the letter set allows it, and the 3-letter word criterion allows it). So the dictionary seems to be global, not per puzzle. That makes sense, for it would be very annoying if word acceptance changed from puzzle to puzzle. Still, this is only a plausible observation; I have not tested it rigorously. Peoplefun has created a rich environment around Wordscapes, including teams, tournaments, prizes, and so on. Coins, hints, blocking of ads, etc. can be purchased with real money. All of that is irrelevant to my goal, finding out whether puzzles are repeated. Peoplefun holds the trademark and/or copyright for Wordscapes, although notice does not seem to appear prominently. ----- 10. Bonus words, 3-letter words, and wordscapescheat.com The wordscapescheat.com web site has been vital for this project, but it has a few shortcomings. The biggest one is that it has no explicit indication of whether a puzzle allows 3-letter words. Each puzzle either allows or rejects 3-letter words. If they are rejected, they are rejected both as answer words and as bonus words. Nevertheless, wordscapescheat.com lists 3-letter words as bonus words even if the puzzle rejects them. This makes it hard to rely on their list of bonus words. (The first level that rejects 3-letter words is 140. After that, each level accepts or rejects 3-letter words, in no pattern that I have noticed.) One work-around is to examine the list of answer words for a puzzle. If it contains no 3-letter words, it is plausible that the Wordscapes puzzle rejects 3-letter words, and any 3-letter words among the bonus words in wordscapescheat.com should be ignored. I have not seen any exception to this method, although I have tested it only on scattered cases, nowhere near all 2580 levels. Another minor shortcoming of the bonus word lists in wordscapescheat.com is the word CINE. It does not appear as an answer word in levels 1-2580, but is accepted as a bonus word in all 46 levels that have C, I, N and E in their letter set. Wordscapescheat.com does not list CINE as a bonus word for any of those 46 levels. The problem with this is not so much the one word CINE, as the uncertainty it casts on the completeness of bonus word lists in wordscapescheat.com. - - - - - Does every puzzle have some bonus words? The short answer is no. But this is a difficult subject. Levels 1-8 have no bonus words in wordscapescheat.com. They are so simple that it is fairly easy to check that there are no other common English words. The best candidate might be ARF, a dog's bark. Levels 1-8 are: 1 (A C T) ACT CAT 2 (N O W) NOW OWN WON 3 (A E R) ARE EAR ERA 4 (A P T) APT PAT TAP 5 (D I P R) DIP DRIP RID RIP 6 (A F I R) AIR FAIR FAR FIR 7 (D E N T) DEN DENT END NET TEN TEND 8 (A K P R) ARK PAR PARK RAP The next puzzle with no bonus words in wordscapescheat.com is level 200: 200 (A C C I T T) ACT ATTIC CACTI CAT TACIT TACT TACTIC TIC Now there's a problem with the name of a type of small bird, TIT. TIT is not an answer word for any level 1-2580, nor is TITS. But Wordscapes does accept TIT as a bonus word for level 200. In fact, among levels 1-2580, there are 57 levels with letter sets containing I and two T's. Of those, 26 disallow 3-letter words, but the other 31 accept TIT as a bonus word. Further, 14 of those 57 also have S in their letter set, and all 14 accept TITS as a bonus word. For each of those 57 levels (82, 182, 200, ..., 2267, 2398, 2535), wordscapescheat.com does not have TIT or TITS in the bonus word list. This makes solid conclusions about bonus words a challenge. With the wordscapescheat.com bonus lists just mostly correct, who knows whether there are other words that Wordscapes will accept? The only way to be sure is probably to reverse engineer the Wordscapes app, not an appealing task for so unimportant a question. There probably are some levels (besides 1-8) that really have no bonus words. Level 715 looks like a good candidate: 715 (G L N P U U) GNU GULP GUN LUG LUNG PLUG PUG PUN UNPLUG A final comment on TIT and TITS is that they may be an example of words that Peoplefun chose to accept as bonus words, but never place in a puzzle as an answer word. ----- 11. Background images The background images in Wordscapes are beautiful, often stunning. They are mostly landscapes, with some closeups of plants. There seems to be no identification, attribution, credit, or way to download these images on the Wordscapes game; or, as far as I can tell, on the Peoplefun web site. Some clever people have captured them and posted them on the internet, a useful source for computer screen backgrounds or personal photo displays. Some backgrounds have animation, such as birds flying by; rain, snow, or leaves falling; or clouds and fog drifting by. These add depth and realism to the images, but some users have complained on the internet that the motion distracts them from the puzzle. The image Hills: Above (levels 1777-1792) fascinates me. They are the Chocolate Hills in the Bohol province of the Philippines, and their origin is unusual (see Wikipedia). Thanks to Irvin Schick for identifying these. Another favorite is Canyon: Pillar (levels 145-160), repeated as Passage: Spire (levels 2545-2560). What is that feature on the left pillar, roughly between the letter circle and the bullseye? It looks a bit like a door! I like to imagine that adventurous rock climbers carved out a small chamber, perhaps stocked with emergency supplies. Or that they installed a door, with nothing behind it, as a prank! These pillars are quartz sandstone formations in the Zhangjiajie National Forest Park, Hunan Province, China. ----- 12. Glossary accepted word -- a word that is either an answer word or a bonus word; it is not rejected by the game. answer word -- a word that appears in the puzzle layout. bonus word -- a word that does not appear in the puzzle layout, but the game accepts it and, when the puzzle is solved, credits a game coin for each bonus word. early -- levels 1-80, which have letter sets of 3, 4, or 5 letters. island word -- an answer word that appears by itself in the layout, not crossed with any other word. Apparently, at most one per puzzle. keyword -- an answer word that uses all the letters in the letter set. In the rare case of two such words, the alphabetically earlier one. layout -- the pattern of letters, in criss-crossing rows and columns. letter set -- the letters available to make words in a puzzle. Some letters may appear 2 or more times. Words can use only as many as appear in the letter set. The letters are shown in a circle. level, puzzle -- a label for a puzzle, starting at 1 and going up. Level and puzzle are used interchangeably. mainstream -- levels after the first 80; see "early". vortex -- a sub-pattern in a layout consisting of 4 letters in a 2 by 2 square. Wordscapes puzzles seem to never have a vortex. Note: Several of these terms I coined for this paper: "accepted word", "early", "island word", "keyword", "layout", "letter set", "mainstream" and "vortex". Others are in common usage for Wordscapes. ----- CURIOSITIES ----- 13. A tale of LARCH and TUPELO As maker, Peoplefun gets to decide what words are accepted. But every player surely has a word or two that they really think should be OK, but is rejected. Here are mine. Working the puzzles, I was irked a few times when I tried to enter LARCH. It's a perfectly good tree name! Why should it be rejected? I made a casual effort to list common types of trees in the northeast USA. Any with more than 7 letters, like sweetgum, were out. Nine names indeed appear among answer words in puzzle levels 1-2580: beech - answer word in 1 level, 1685 elm - answer word in 20 levels, 63, 78, 88, etc. fir - answer word in 18 levels, 6, 82, 100, etc. hickory - answer word in 1 level, 1974 locust - answer word in 2 levels, 352, 1812 oak - answer word in 3 levels, 1539, 1629, 2543 pine - answer word in 6 levels, 901, 1049, 1136, etc. poplar - answer word in 1 level, 1422 willow - answer word in 1 level, 714 Another 7 tree names do not appear among the answer words, but a check of letter sets finds that none of the levels 1-2580 has the letters needed to make these names; so it is no surprise they don't appear: aspen - no letter sets birch - no letter sets cherry - no letter sets dogwood - no letter sets (update: answer word in level 2611) maple - no letter sets spruce - no letter sets walnut - no letter sets This leaves two names on my informal list, TUPELO and LARCH. Just one puzzle has the letters needed for TUPELO, plus a second L: level 2505, letter set E L L O P T U, has 10 answer words: LOPE LUTE PELT POET POLE POLL POLLUTE PULL TELL TOLL (3-letter words are not allowed) and TUPELO is not accepted as a bonus word. Three puzzles have the letters needed for LARCH, plus the letter O: levels 140, 668 and 2206, all have letter set A C H L O R; 140 has 8 answer words (3-letter words disallowed) 668 has 14 answer words (3-letter words allowed) 2206 has 12 answer words (3-letter words allowed) but none of these accept LARCH as answer or bonus. So these two tree names, LARCH and TUPELO, could be accepted by the respective puzzles; but they are not, to my chagrin. While we're talking about word restriction, money names seem to be slanted toward American and modern European. CENT appears in 22 answer word sets PENNY in none NICKEL in one (level 1262; it can also mean the metal) DIME in 11 answer word sets QUARTER in one (level 2422; it can also mean a fraction, or verb) DOLLAR in one (level 1131) EURO in 13 answer word sets PENCE in none POUND in one (level 1342; it can also mean weight, or verb) FRANC in none MARK in 3 answer word sets (but means much besides German currency) PESETA in none PESO in none LIRA in none YUAN in none YEN in 13 answer word sets (but surely as an English word!) RUBLE in none The letters for PESO appear in 19 puzzles (193, ..., 2554), and PESO is not accepted as a bonus word in any of them. But here's a surprise: the letters for RUBLE appear in the letter set of 7 puzzles. In all 7, RUBLE is accepted as a bonus word! (Levels 1006, 1063, 1504, 1568, 2212, 2248 and 2569.) British spelling (colour, flavour, humour, labour) is absent in the answer words, but no letter set in levels 1-2580 has the letters required for these words. However, level 1145 has letter set A F O R U V, and its answer word set includes both FAVOR and FAVOUR! ----- 14. No vortex in the layout Crossword puzzles, especially the difficult ones, have lots of cross linking. Wordscapes, in contrast, is sparse. I have never seen a Wordscapes puzzle with 4 letters in a 2-by-2 square. But that doesn't mean there are none. They are not hard to construct by hand, such as this one: . . . I . . . . . T . . T I M E . . . . E M I T . . N . . . I call this pattern a "vortex" because it has words coming in from various directions. This example is a clockwise vortex, and there can be a counterclockwise vortex, the mirror image. The letter set in this vortex, E I M N T, occurs as a (sub)set of just one Wordscape puzzle in levels 1-2580: level 1531, E I M N T U. Allowng the bonus words would make our task even easier: MENU MIEN MINUET NUT TEN TINE TUN But suppose we limit ourselves to the answer words of that puzzle: EMIT EMU ITEM MEN MET MINE MINT MINUTE MITE MUTE NET NIT TIE TIME TIN TUNE UNIT UNITE UNMET UNTIE We can make a Wordscapes-like layout that looks plausible: . . . U . M I N E . . . . . N . U . . . . . . . M I N T . . . . . . . . T . E M U . . . . . . . . . . N E T . U N T I E . . I . I . N . . . . . . T U N E M . M I N U T E . . . E . . T . . . . . . . T I M E . . . . . . . . . E M I T . . . . . . . N . . . . . . . . But the level 1531 solution does not contain a vortex. Wordscapes words are highly constrained, to be formed from just the letter set for the given puzzle. To make a vortex, two words must have their beginning two letters, and another two words their ending two letters, coincident. Each of the four letters in the vortex appears in two of the four words. Together with the limitation of the letter set, this makes it plausible that most Wordscapes puzzles cannot form a vortex. I bet that either the Wordscapes generator is coded such that a vortex is impossible, or that the generation process makes it very unlikely that a vortex would arise. To evaluate whether the makers intentionally avoid vortexes, we can ask how many of the answer word sets are capable of making a vortex. As may be obvious to crossword experts, every clockwise vortex has a corresponding counterclockwise vortex; the number of them is the same. Suppose we have words 11wx, 22xz, yz33 and wy44. These make a clockwise vortex: . . . 2 . . . . . 2 . . 1 1 w x . . . . y z 3 3 . . 4 . . . . . 4 . . . And also a counterclockwise vortex, in this diagram simply the above vortex reflected across a \ diagonal: . . 1 . . . . . 1 . . . . . w y 4 4 2 2 x z . . . . . 3 . . . . . 3 . . Therefore, we count only the vortices of one type, say, clockwise. The results surprised me. Of levels 1-2580, 1244 levels make no vertices, about 48%; but the other 1336 (52%) do make vortices! How many vortices? That is surprising too. 78 levels make just one vortex. 113 make two vortices, the largest number that make a given number. 72 levels make 3 vortices. 83 levels make 4 vortices, and so on. The smallest number of vortices no level makes is 73. The largest number of vortices made by 2 levels is 317 (levels 1371 and 2183). The second largest number of vortices made by any level is 446 (level 1971). The largest number of vortices made by any level is 507 (level 1330). The first level to make vortices is level 11, and it makes 8 vortices. The first level to make just 1 vortex is level 26. Its vortex is: . . A . S A P . . S E A . K . . Overall, levels 1-2580 make a total of 40026 vortices, for an average of 40026/2580 = 15.5 vortices per level, or 40026/1336 = 30.0 vortices per level that make any at all. The abundance of possible vortices convinces me that if they were present in Wordscapes, I would have seen them. So I believe they are absent. Further, I believe the puzzle generator specifically avoids vortices. ----- 15. Sizes and stats The size of a game layout is important to a game designer. It must fit on the screen of the intended device, yet be big enough to be read easily. For players, the size is at most a curiosity. Informally, I noted some of the largest Wordscapes layouts I noticed. It's not a thorough survey, but it does suggest the limits. I found these sizes, width by height: 13 W x 13 H -- levels 1758, 1820, 1932, 1987, 2166, 2288, 2358, 2482, 2546 14 W x 12 H -- levels 1716, 1791, 1920, 2182, 2234 14 W x 13 H -- levels 2244, 2296, 2448, 2460 15 W x 11 H -- levels 1409, 1964 15 W x 12 H -- level 1680 15 W x 13 H -- levels 2148, 2420 The maximum width may be 15, and the maximum height may be 13. - - - - - What is the largest average length of answer words in a puzzle? Level 208 has average length 5, matched by 732, 759, 772, ...; Level 862 has average length 5 1/4, unmatched until exceeded by: Level 2262 has average length 5 2/7, matched by 2348 and 2512. (Note, this is a record that might be broken by some level beyond 2580.) Checking the above record: 2262 FREE FREER FREEZE FREEZER REEF REEFER REFER 2348 DEED DELUDE DELUDED DUDE DUEL DUELED ELUDED 2512 DEGREE EDGE EDGER EGRET GREED GREET GREETED Although these have different numbers of words with 4, 5 and 6 letters, they all have a total of 37 letters and 7 words, for an average of 5 2/7 letters per answer word. - - - - - How many answer words can a puzzle have? The following table shows the number of puzzles with a given number of answer words. #words #puzzles first level 2 1 1 3 3 2 4 4 5 5 9 9 6 194 7 7 232 12 8 237 11 9 282 20 10 255 27 11 233 63 12 216 46 13 167 87 14 161 78 15 122 136 16 106 115 17 99 132 18 62 134 19 58 236 20 139 232 (29631 answer words over all (2580) puzzles processed, yields overall average 11.48 words per puzzle.) Is 20 words per puzzle an arbitrary limit, or the most that can fit? Consider level 232, where 20 words is first seen: 232 A E L R T T ALERT ALTER ARE ART EAR EARL ERA LATE LATER LATTER LET RAT RATE RATTLE REAL TALE TAR TART TEAR TREAT A bonus word, EAT, that is used as an answer word in 28 puzzles, could be added, for 21 answer words: . . . L A T E . E . . . . . . . . R . R E A L . . . . R A T E . A . R . . . . . . R . . . . . . . . . . L E T . . T A R T . . . L . A . . . A . A . . . . A . R A T . L . T E A R . T . L . A L E R T . L . . E . . . R . . . L A T T E R . . . . . . . E . E . a . . T R E A T . . . R . t . - - - - - What are the smallest answer words, and how often do they occur? Wordscapes uses words of 3 through 7 letters. But some puzzles do not use 3-letter words (and apparently those are just the ones that disallow 3-letter words). Such puzzles might have 4-letter words as the smallest, but might there be puzzles that do not have any 3- or 4-letter answer words? No, each puzzle (levels 1-2580) has an answer word shorter than 5 letters: smallest answer word has 3 letters: 1208 puzzles smallest answer word has 4 letters: 1372 puzzles This table shows the number of answer words of each length: length: 3 4 5 6 7 #words: 7200 15004 4369 2040 1018 Over all the 2580 puzzles processed, 29631 words with total 122827 letters, yields an overall average word length of 4.145 letters. - - - - - How common are the different sizes of letter sets? The following table shows the number of letters in the letter set. 3 letters: 4 puzzles, first level 1, final level 4 4 letters: 8 puzzles, first level 5, final level 12 5 letters: 68 puzzles, first level 13, final level 80 6 letters: 1490 puzzles, first level 81, final level 2580 7 letters: 1010 puzzles, first level 483, final level 2579 - - - - - What is the largest accepted word set? An interesting question, but beyond the reach of this project. However, one of the larger ones, especially among levels that disallow 3-letter words, must be level 2252. It has 17 answer and 23 bonus words, for a total of 40: answer words: CLOSE CLOSEST CLOSET CLOT COLT LESS LEST LETS LOSE LOSS LOST LOTS SETS SLOT SOLE STOLE TOSS bonus words: CELT CELTS CESS CLOSES CLOSETS CLOTS COLTS COST COSTS COTE COTS LOESS LOSES SCOTS SECT SECTS SLOE SLOTS SOCLE SOLES STOLES TOES TOLE - - - - - How common are multiple letters? 720 of the 2172 distinct letter sets (in levels 1-2580) contain no repeated letters. The alphabetically first and last few are: A B C D E K - level 2575 A B C E H K O - level 1176 A B C E H L - levels 120, 444, 1909 A B C E N O - levels 504, 1178 ... M O R S T Y - level 318 N O P T U W - level 308 N O T U - level 9 N O W - level 2 23 letters of the alphabet appear doubled in letter sets; only J, Q and X do not. 14 letters of the alphabet appear tripled in letter sets; C, F, H, J, K, Q, U, V, W, X, Y and Z do not. Only one letter appears quadrupled in a letter set. That is E, in level 1461 (letter set E E E E F R R), and the one word that uses all four Es is REFEREE. ----- 16. Multiple keyword candidates Some puzzles have more than one accepted word that is made using all the letters of the letter set. If only one of these is an answer word, the other(s) being bonus words, all is well; that one is the keyword. A few puzzles have two or more answer words that use all the letters. In that case, I arbitrarily use the word that is alphabetically earliest, to be the keyword. Multiple candidate keywords are fairly common (19 cases) in levels 1-80, where there are only 3, 4 or 5 letters in the letter set. Considering only the mainstream levels 81-2580, we find 88 cases: 2 candidate words of 6 letters: 71 cases, levels 106, ..., 2556 level 106: DENIED INDEED level 2556: INSULT SUNLIT 2 candidate words of 7 letters: 8 cases, levels 527, ..., 2108 level 527: LOOKOUT OUTLOOK level 2108: PERFECT PREFECT 3 candidate words of 6 letters: 8 cases, levels 115, ..., 2530 level 115: CALLER CELLAR RECALL level 2530: EARNED ENDEAR NEARED 4 candidate words of 6 letters: 1 case, level 373 level 373: RETEST SETTER STREET TESTER Just as a puzzle can have more than one answer word of maximal length, one or more of the bonus words can also be of maximal length. A few such anagram cases that I noticed are: level answer word(s) bonus word(s) ----- -------------- ------------- 1417 BEGGAR BAGGER 2338 ASCEND DANCES 2497 GREASE AGREES 2543 TAKEOUT OUTTAKE 2202 MEREST METERS, METRES 2489 LIVELY EVILLY, VILELY 1975 CITRUS, RUSTIC RICTUS 2412 LUSTER, RESULT, RUSTLE LUSTRE, SUTLER ----- 17. How often specific answer words occur Wordscapes uses the same short words in many puzzles. That's not surprising, considering there are not many of them. In levels 1-2580, 6308 different words appear as answer words. Let's exclude the early levels 1-80, with their small (3, 4 and 5) letter sets, that may skew the counts toward short words. Anong levels 81-2580, slightly fewer (6274) different words appear as answer words. Of the 6274 words, 2678 appear only once. The lengths of those are: 23 are 3-letter words (BIZ FEW HEX ... ZAP ZIG ZIT) 215 are 4-letter words (AMOK AMPS APEX ... ZINC ZITI ZOOS) 602 are 5-letter words (ABASE ABBOT ABIDE ... YACHT YEAST YELLS) 1060 are 6-letter words (ABACUS ABOUND ABSURD ... YOGURT ZAPPED ZENITH) 778 are 7-letter words (ABALONE ABILITY ABSCESS ... WRIGGLE ZEALOUS ZILLION) Of the 6274 words: 2678 appear 1 time (see above) 993 appear 2 times 545 appear 3 times 313 appear 4 times 232 appear 5 times 222 appear 6 times 159 appear 7 times 151 appear 8 times 101 appear 9 times 117 appear 10 times 763 appear more than 10 times Of the 6274 words, the words of each length that appear most are: 7-letter words: 10 words appear 3 times (ANGULAR CANTEEN ... SCIENCE TRIVIAL) 6-letter words: 3 words appear 5 times (REPENT SCENIC SIMMER) 5-letter words: 1 word appears 17 times (ENTER); next is 14 times (REUSE) 4-letter words: 10 words appear 40 or more times (see below) 3-letter words: 12 words appear 40 or more times (see below) The 4-letter words that appear 40 or more times are: 40 times: REEL SIRE 41 times: LEER RISE 43 times: DEER 44 times: RITE TIER 45 times: TIRE 46 times: TREE 51 times: SEER The 3-letter words that appear 40 or more times are: 40 times: ERR 41 times: EAR 42 times: ERA RED SEE SUE TIE 44 times: USE 45 times: ALE ORE 51 times: LIE 58 times: IRE I am sure that regular Wordscapes players will view these lists of often used 3- and 4-letter words without surprise, as familiar friends. Do any puzzles use all of, say, the top 10 most common 3-letter words? Not even close. Not even one puzzle uses IRE, LIE and ALE. Only 6 puzzles use both IRE and LIE: levels 500, 957, 1825, 1949, 2035 and 2569. How about the most common 4-letter words? None use all of the top three, SEER, TREE and TIRE. But 10 puzzles do use both SEER and TREE: levels 373, 884, ..., 2202 and 2260. It seems that using several of the most common answer words, is uncommon. But how well do the top several words cover the range of puzzles? The top 10 3-letter words (ERA through IRE) appear in 624 of levels 1-2580, about 24%. (Here we include the early puzzles, level 1-80.) The top 10 4-letter words appear in only 225 puzzles, about 9%. ----- 18. Are daily puzzles repeats? Besides the standard series of Wordscapes puzzles, the Wordscapes web site presents a daily puzzle. This puzzle is available only for 24 hours; after the day is gone, so is its daily puzzle, replaced with another puzzle for the next day. Once you complete today's puzzle, you cannot replay it. So, are these daily puzzles repeats of puzzles in the standard series? To get an approximate answer to that question, I captured the daily puzzle for the final two weeks of 2021. 14 cases is only suggestive, but if dailies are mostly or all repeats, that should show up. Fortunately, wordscapescheat.com also has the daily puzzle solution, with bonus and answer word lists, although it also disappears at the end of each day. 13 of the 14 dailies had the same letter set and accepted words as one or two standard series puzzles. (Except, if 3-letter words are allowed in one puzzle but not the other, the accepted words are accordingly different.) However, the words chosen from accepted words to be answer words, varied from the standard puzzles, and the layouts were very different from the standard puzzles. The table below shows the December date of each daily, the level of the one or two puzzles with the same letter set, and for each of these puzzles, the number of answer words, and whether 3-letter words were allowed. It seems that daily puzzles come from the same mine as standard series puzzles (so to speak), but are distinct puzzles. (Even when the answer word sets are identical, as in December 18 and level 2081, or December 25 and level 889, the layouts are very different.) Dec date 18 19 20 21 22 23 24 # answer 8 14 9 10 17 9 16 3-letter yes yes no no yes no no level #1 2081 1687 717 586 939 768 496 # answer 8 12 11 15 6 9 14 3-letter yes yes yes yes no no yes level #2 --- --- 1391 2016 2177 1818 1268 # answer --- --- 11 9 15 8 13 3-letter --- --- yes no yes no yes Dec date 25 26 27 28 29 30 31 # answer 10 13 16 18 9 10 8 3-letter no yes yes yes yes no no level #1 889 283 1146 354 1454 1419 --- # answer 10 10 14 10 8 8 --- 3-letter no yes yes no no no --- level #2 --- --- --- 1833 --- --- --- # answer --- --- --- 9 --- --- --- 3-letter --- --- --- no --- --- --- The daily for December 31 is a surprise. Its letter set (D F L N O U) does not occur among levels 1-2580. Perhaps it is a completely new puzzle, but I suspect it shares a letter set (and most of its answer words) with some puzzle beyond level 2580. A research challenge for you, dear reader! (The next day, January 1, 2022 was usual: the same letter set as level 262, and a very different layout.) ----- TEDIOUS SUPPORTING DATA ----- 19. List of nearly same answer word sets Here is a list of all pairs of puzzles, levels 1-2580, in which the set of answer words differs by exactly one word. This includes both cases were one set is the same as another except for one additional word, and cases where the number of words is equal but one set has one word and the other has a different word. An example of the former is levels 224 and 1951. Their answer word sets are: 224 ARCH BARN BRAN BRANCH CARB CRAB RANCH 1951 ARCH BARN BRAN BRANCH CARB CHAR CRAB RANCH This case is summarized in the list below as: 224, 1951 - 1951 adds CHAR (It could be said that level 224 "subtracts" CHAR from level 1951's larger set, but I chose to summarize these cases as which adds to the smaller set.) An example of the latter is levels 121 and 2053. Their answer word sets are: 121 CHORUS CRUSH HOUR OUCH OUR OURS RUSH SOUR SUCH 2053 CHORUS CRUSH HOUR OUCH OURS RUSH SCOUR SOUR SUCH This case is summarized in the list below as: 121, 2053 - 121 has OUR, 2053 has SCOUR Only one puzzle appears more than once in this list, level 703: 293, 703 - 293 adds REEK 703, 1955 - 1955 adds REEK The list is in two parts, corresponding to the two kinds of case above. There are 52 cases where one puzzle adds a word, and 14 cases where the sets have the same number of words but one word differs in each. 224, 1951 - 1951 adds CHAR 235, 2149 - 235 adds TRIPS 242, 592 - 592 adds RUE 293, 703 - 293 adds REEK 314, 2084 - 2084 adds LAUD 348, 2138 - 348 adds PEERS 354, 1833 - 354 adds SEER 404, 1501 - 1501 adds EMU 437, 630 - 437 adds BUY 465, 462 - 465 adds GNU 471, 1663 - 1663 adds CON 473, 1931 - 1931 adds PIES 510, 578 - 578 adds OFT 513, 2031 - 2031 adds TIE 566, 2029 - 2029 adds ROIL 576, 1340 - 1340 adds COOP 598, 1829 - 598 adds OUT 612, 1716 - 1716 adds AIOLI 613, 791 - 791 adds SNOOP 638, 1254 - 1254 adds ORCA 647, 1757 - 1757 adds PEP 651, 1435 - 1435 adds TREE 674, 1774 - 1774 adds SOON 684, 1444 - 684 adds SELL 694, 2389 - 694 adds OOH 703, 1955 - 1955 adds REEK 730, 1837 - 730 adds TICS 743, 2145 - 743 adds SUIT 746, 1861 - 1861 adds GOAL 756, 2016 - 756 adds RICE 768, 1818 - 768 adds TREE 772, 2130 - 2130 adds MALL 777, 1789 - 1789 adds TEES 782, 1863 - 1863 adds BOAR 789, 1967 - 789 adds GILT 796, 1764 - 1764 adds HORN 810, 2077 - 810 adds CORE 811, 2139 - 2139 adds COPE 816, 1988 - 816 adds CULT 826, 2178 - 826 adds SINE 828, 2092 - 828 adds PEER 832, 2350 - 832 adds BISCUIT 833, 2169 - 2169 adds CON 836, 1045 - 836 adds AFFABLE 838, 2192 - 838 adds MANGY 860, 2176 - 860 adds ANTI 1009, 2234 - 2234 adds RAN 1064, 2028 - 2028 adds NOMINAL 1113, 2221 - 1113 adds DRAM 1130, 1580 - 1580 adds TUBULAR 1327, 2383 - 1327 adds REM 1361, 1821 - 1361 adds LEGALLY 121, 2053 - 121 has OUR, 2053 has SCOUR 357, 450 - 357 has RYE, 450 has PER 484, 1799 - 484 has PET, 1799 has PUCK 548, 1135 - 548 has IRE, 1135 has CUR 572, 1902 - 572 has ONE, 1902 has NOEL 610, 769 - 610 has OAR, 769 has CUR 632, 1410 - 632 has ALL, 1410 has LAB 717, 1391 - 717 has MIL, 1391 has ELM 741, 2079 - 741 has MOAN, 2079 has NOW 771, 2102 - 771 has ORE, 2102 has BED 867, 2231 - 867 has PYRE, 2231 has RUE 943, 2225 - 943 has TINE, 2225 has NICE 989, 1541 - 989 has RARELY, 1541 has YEARLY 1637, 2436 - 1637 has GENT, 2436 has TEENAGE ----- 20. List of levels with same answer word set Here are the level numbers and answer words, for the 49 pairs of puzzles within levels 1-2580, that have the same answer word set. They are listed in order of the larger level number, which appears second. This way, the list up to any given entry contains exactly all such pairs when the search space is limited to levels 1 through that entry's larger level. If more levels are added to the analysis, they will append pairs to this list, never insert newly discovered pairs between those here. 527, 573 LOOK LOOKOUT LOOT LOT OUT OUTLOOK TOO TOOK TOOL 498, 582 ACT ATTIC CAST CAT ITS SAC SAT SIT STAT STATIC TACIT TACT TIC TIS 265, 626 CANS CASINO COIN CONS ICON IONS SCAN SCION SONIC 280, 636 FIRS FIRST FISH FIST FITS HITS RIFT SHIFT SHIRT SHRIFT SIFT STIR THIS 654, 673 DEN DENSE END NEED SEE SEED SEEN SEND SNEEZE SNEEZED 618, 780 ICES NICE NIECE SCENE SCENIC SCIENCE SEEN SINCE SINE 428, 1345 BLOUSE BLUE BUS LOB LOBE LOSE LOUSE LUBE SLOB SOB SOLE SOUL SUB SUE USE 526, 1553 EELS ELSE LENS PEEL PENS SEEN SEEP SLEEP SPLEEN 570, 1721 CORE FOES FORCE FORE FRESCO ORES REFS ROSE SCORE SORE 705, 1737 AMMO ATOM MAMMOTH MATH MOAT MOMMA MOTH OATH 479, 1771 EIGHT EIGHTH GET GIT HEIGHT HIGH HIT THE THIGH 785, 1775 HITS ITCH SWITCH THIS TICS WHIT WISH WITCH WITH WITS 762, 1782 FIFTY FIST FITS FLIT IFFY LIFT LIST SIFT SILT SLIT STIFF STIFFLY 330, 1783 NEON NONE OWNER RENOWN WORE WORN WREN 764, 1792 GRIN IRES REIGN RESIGN RESIN RIGS RING RINSE RISE RISEN SIGN SINE SING SINGE SIRE SIREN 286, 1798 BEER BEET BELT BERET LEER REBEL REEL TREBLE 725, 1834 BIDE BIRD BRED BRIDE BRIDGE BRIE BRIG DIRE DIRGE GRID RIDE RIDGE 758, 1877 ENQUIRY INURE QUERY REIN RUE RUIN RUN RUNE RYE URN YEN YIN 250, 1889 BEND BLED BLEND BLUE BUNDLE DUEL DUNE LEND LUBE NUDE 382, 1893 ANTE ANTI INANE INNATE NEAT NINE TINE 440, 1894 HEIR HERS HIKE HIKER HIRE IRES IRKS RISE RISK SHIRE SHIRK SHRIEK SIRE SKIER 731, 1935 AIL AIM ANY INLAY LAIN LAM LAY MAIL MAIN MAINLY MAN MANLY MAY MIL NAIL NAY NIL YAM YIN 786, 1950 FLESH FLUE FLUSH FUEL FUSE HUES HUFF LUSH SELF SHELF SHUFFLE 871, 1953 ALLAY ALLY AWAY HALL HALLWAY WALL 293, 1955 EVER EVOKE OVER REEK REVOKE ROVE VEER 766, 1966 ACCEDE ACED ACNE CADENCE CANE CEDE DANCE DEAN NEED 748, 1972 HOLY HOST HOTLY LOST LOTS ROSY ROTS SHORT SHORTLY SHOT SLOT SLOTH SORT STORY TOYS 282, 1978 GOPHER GORE GROPE HERO HOPE OGRE PORE REPO ROPE 813, 1979 CHEF CHIEF CHIEFLY CHILE FILE LICE LIFE 800, 1980 AIMS HAMS HISS MASH MASS MISS SASH SASHIMI SHAM SMASH 869, 1981 ARDOR ARMOR DORM DRAM RAMROD ROAD ROAM ROAR 360, 2011 ELFIN FEEL FELINE FILE FINE FLEE LIEN LIFE LINE 728, 2018 CITE EMIT ITEM MICE MIME MIMETIC MIMIC MITE TIME 351, 2039 ARMOR ATOM MART MOAT MORTAR ROAM ROAR TRAM 759, 2040 ABOARD ABROAD BARD BOAR BRAVADO BRAVO BROAD DRAB ROAD 747, 2065 CORE CORRECT CROC RECTOR RETRO ROTE TORE 734, 2072 CLUE CUES CUFF FLUE FUEL FUSE SCUFF SCUFFLE SELF 398, 2098 ETHOS HOES HOOT HOSE HOST SHOE SHOO SHOOT SHOT SOOT SOOTH SOOTHE THOSE TOES 165, 2103 ALONG ANALOG ANGLO GALA GOAL LOAN LONG 722, 2122 ICES ISLE LICE LICK LIES LIKE SICK SICKLE SILK SLICE SLICK 872, 2162 EARL LEAVE LEER LEVER RAVE RAVEL REAL REEL REVEAL REVEL VALE VEAL 987, 2186 AGED DAGGER DARE DEAR DRAG GEAR GRAD GRADE RAGE READ 367, 2197 DELUXE DUE DUEL EEL ELUDE EXUDE LED 865, 2198 ACID ACIDLY CLAD CLAY DAILY DIAL IDLY LACY LADY LAID 1030, 2208 ACHE ACHIEVE CAVE CHIVE EACH HAVE HEAVE HIVE VICE 978, 2216 BELL BELLOW BELOW BLEW BLOW BOLL BOWL CELL CELLO COWBELL COWL ELBOW LOBE WELL 666, 2302 CEDE DECEIVE DEVICE DICE DIVE ICED VICE VIED 503, 2317 DIAL INLAND LAID LAIN LAND NAIL 658, 2375 DAME DEAF DEMO DOME FADE FAME FAMED FOAM FOAMED MADE MEAD MODE ----- 21. Keyword intersections for 49 pairs with same answer word set For each pair of puzzles with identical answer word sets, the list below shows the words that the keyword intersects, in the order that those intersections occur. 527 - LOOKOUT intersects LOOK, OUT, TOOL, OUTLOOK 573 - LOOKOUT intersects LOOK, OUTLOOK, OUT 498 - STATIC intersects STAT, TACIT 582 - STATIC intersects SIT, ACT 265 - CASINO intersects IONS 626 - CASINO ibtersects COIN, SONIC 280 - SHRIFT intersects FIRS, SHIRT, RIFT 636 - SHRIFT intersects FITS, STIR, SHIRT 654 - SNEEZED intersects NEED, DENSE 673 - SNEEZED intersects SEEN, DENSE, END 618 - SCIENCE intersects SCENIC, SCENE, SEEN 780 - SCIENCE intersects SCENIC, NIECE, SCENE 428 - BLOUSE intersects LOUSE 1345 - BLOUSE intersects SLOB, SOLE, BLUE 526 - SPLEEN intersects PENS, SEEN 1553 - SPLEEN intersects SLEEP, ELSE 570 - FRESCO intersects FORCE, ROSE, CORE 1721 - FRESCO intersects FORE, SORE, FOES 705 - MAMMOTH intersects MOMMA, AMMO, OATH 1737 - MAMMOTH intersects MOMMA, OATH 479 - EIGHTH intersects THIGH, GIT 1771 - EIGHTH intersects HIGH, HIT 785 - SWITCH intersects THIS, WITS, WITCH 1775 - SWITCH intersects WITS, WITCH 762 - STIFFLY intersects SILT, LIFT 1782 - STIFFLY intersects STIFF, SILT 330 - RENOWN intersects WORN, NEON, WREN 1783 - RENOWN intersects WREN, WORN 764 - RESIGN intersects SINGE 1792 - RESIGN intersects REIGN, SINGE 286 - TREBLE intersects BERET, BELT, REBEL 1798 - TREBLE intersects BELT, REBEL 725 - BRIDGE intersects BRIDE 1834 - BRIDGE intersects BIRD, BRIDE, RIDGE 758 - ENQUIRY intersects RUN, QUERY 1877 - ENQUIRY intersects QUERY, RYE 250 - BUNDLE intersects BEND, DUEL 1889 - BUNDLE intersects BLEND 382 - INNATE intersects ANTI, INANE 1893 - INNATE intersects ANTI, INANE 440 - SHRIEK intersects HIKER 1894 - SHRIEK intersects RISK, HIKE 731 - MAINLY intersects NAIL, LAY 1935 - MAINLY intersects NAIL, LAY 786 - SHUFFLE intersects SHELF, FLUE 1950 - SHUFFLE intersects SHELF, FLUE 871 - HALLWAY intersects HALL, ALLAY, WALL 1953 - HALLWAY intersects HALL, ALLAY, WALL 293 - REVOKE intersects ROVE, EVOKE, VEER 1955 - REVOKE intersects EVOKE 766 - CADENCE intersects ACCEDE 1966 - CADENCE intersects ACCEDE, DANCE, ACED 748 - SHORTLY intersects SLOTH, STORY 1972 - SHORTLY intersects SLOTH, STORY 282 - GOPHER intersects GROPE, HERO 1978 - GOPHER intersects REPO 813 - CHIEFLY intersects FILE 1979 - CHIEFLY intersects CHIEF, FILE 800 - SASHIMI intersects MASS 1980 - SASHIMI intersects SASH, MASS 869 - RAMROD intersects ARDOR, DRAM, ROAM 1981 - RAMROD intersects ROAD, ARMOR 360 - FELINE intersects LINE 2011 - FELINE intersects FEEL, LIFE 728 - MIMETIC intersects MIMIC, MITE, CITE 2018 - MIMETIC intersects MIMIC, MITE, MICE 351 - MORTAR intersects ARMOR, ATOM 2039 - MORTAR intersects ARMOR, ROAM, TRAM 759 - BRAVADO intersects BRAVO, ABOARD, DRAB 2040 - BRAVADO intersects ABOARD, BRAVO, ROAD 747 - CORRECT intersects CROC, RECTOR, CORE 2065 - CORRECT intersects RECTOR, CORE 734 - SCUFFLE intersects CUES, FUEL, CUFF 2072 - SCUFFLE intersects CUFF, FUSE 398 - SOOTHE intersects SHOO, THOSE 2098 - SOOTHE intersects HOST 165 - ANALOG intersects GALA, ANGLO 2103 - ANALOG intersects LONG, LOAN, GOAL 722 - SICKLE intersects LICK 2122 - SICKLE intersects ICES, LIES 872 - REVEAL intersects RAVEL, REVEL 2162 - REVEAL intersects RAVEL 987 - DAGGER intersects DEAR, AGED 2186 - DAGGER intersects DEAR, AGED 367 - DELUXE intersects DUE, EXUDE, EEL 2197 - DELUXE intersects ELUDE, LED, EEL 865 - ACIDLY intersects ACID, LACY 2198 - ACIDLY intersects CLAD, IDLY 1030 - ACHIEVE intersects CHIVE, VICE, EACH 2208 - ACHIEVE intersects CAVE, CHIVE, VICE 978 - COWBELL intersects COWL, BOLL, BELLOW 2216 - COWBELL intersects COWL, BOLL, BELLOW 666 - DECEIVE intersects ICED, DICE, VICE 2302 - DECEIVE intersects DICE, VICE, CEDE, DEVICE 503 - INLAND intersects LAID, LAIN, DIAL 2317 - INLAND intersects DIAL 658 - FOAMED intersects FOAM 2375 - FOAMED intersects DEMO, DAME, FAMED ===== the end. whew! =====