=============================================================================== Everyday Genius: Square Logic =============================================================================== Title: Everyday Genius: Square Logic Publisher: Mumbo Jumbo Platform: PC Release date: 21 October 2009 =============================================================================== Table of Contents =============================================================================== - A. FAQ/Guide Information [QX00] - B. General Techniques for Solving Boards [QX01] I. Foreword [QX01+0] II. Line Scanning Algorithm [QX01+1] III. Determined But Unsolved Linear Cage [QX01+2] IV. Common And Necessary Equation Element [QX01+3] V. Complete Inequality Balancing Algorithm [QX01+4] VI. Simple Inequality Balancing [QX01+5] - C. Puzzle Variations [QX02] - D. Introductory Walkthrough [QX03] - E. Closing Comments [QX04] - F. Contact Information [QX05] =============================================================================== A. FAQ/Guide Information [QX00] =============================================================================== Everday Genius: Square Logic Guide Current Version 1.1 31 October 2009 Brandon Williams (Sheepdude860, ShEEpDuDE86, Sheepdude123) Release History: Version 1.1 31 October 2009 Updated: Line Scanning Algorithm Added: Determined But Unsolved Linear Cage Common And Necessary Equation Element Complete Inequality Balancing Algorithm Version 1.0 30 October 2009 Added: General Techniques for Solving Boards Puzzle Variations Introductory Walkthrough Closing Comments Contact Information =============================================================================== B. General Techniques for Solving Boards [QX01] =============================================================================== I. Foreword [QX01+0] Solving Square Logic puzzles requires you, the solver, to understand exactly what the computer does and does not automatically do for you. What it DOES DO (if you are using the default settings) is alert you when you have chosen an incorrect solution for a square and when you have eliminated a candidate from a square which was actually the solution. It also automatically eliminates impossible candidates based on the requirement that each digit can and must only appear once in each row and column. What it DOES NOT do is eliminate impossible candidates based on cage rules. It also never selects a solution for a square even if there is an apparent solution; you must do this manually. It is also worth noting that the equation display, while infinitely useful, does not always display accurate possibilities for cages. In fact, many times the computer will give you a list of possible equations, when many of them are in fact clearly impossible for the situation. So, unfortunately, you must parse through the possible equations and deduce which of them are actually possible, and use the result to formulate a possible solution. II. Line Scanning Algorithm [QX01+1] 1. Choose the first row or column. 2. Choose the first available digit. 3. Inspect the candidate list for the row or column for the existence of the current digit. 4. If the digit appears in only one of the squares, choose it as the solution for that square. 5. If the digit appears at least twice, choose the next digit and start at step 3. 6. If all the digits have been checked, choose the next row or column and start at step 2. 7. If all the rows and columns have been checked for all digits, you are done. The line scanning algorithm is essentially the basic Sudoku solving algorithm. Since it takes a long time to complete and usually only yields minimal results, it should be one of your last resorts when solving Square Logic puzzles. However, it is necessary to employ this technique, especially on the more difficult puzzles (such as the final Beyond challenge puzzle), in order to find a solution. If you are stuck and cannot seem to find any solutions, this algorithm will probably help. III. Determined But Unsolved Linear Cage [QX01+2] This technique may be employed when you are certain of the solution of a cage, but uncertain of the order. Consider a situation where two adjacent blocks lie in a 20x cage. The only possible solution for the cage is 4 and 5. Even though you may not know which square contains which number, you may be certain that the two of them combined contain 4 and 5, and therefore you can remove 4 and 5 from the candidate lists of the squares in that row or column. IV. Common And Necessary Equation Element [QX01+3] Similar to the previous technique, you may employ this technique when you are certain that a particular number must occur in a cage due to its presence in all possible solutions. Consider a situation where a 30x cage has three blocks in the same row or column, and the candidates for each square in the 30x cage are 12356. The only possible solutions for the cage are 1x5x6 and 2x3x5. Even though you may not know which solution is correct, since 5 is present in all the solutions for the cage, you can be certain that 5 must occur in that cage. You can therefore eliminate 5 as a candidate from the rest of the squares in that row or column. V. Complete Inequality Balancing Algorithm [QX01+4] 1. Choose an inequality square. 2. Choose the lowest digit from the candidate list of the selected square. 3. For all adjacent squares that are more than the selected square, remove from their candidate list all candidates equal to or less than the selected digit. 4. Choose the highest digit from the candidate list of the selected square. 5. For all adjacent squares that are less than the selected square, remove from their candidate list all candidates that are equal to or more than the selected digit. 6. Choose the next inequality square and start at step 2. 7. Repeat steps 1-6 until no further candidate elimination is possible. This algorithm is confusing and tedious even for small inequality cages, but it becomes necessary on difficult inequality puzzles, such as the final Beyond challenge puzzle. It may be a good idea to start with the simple inequality balancing technique below to partially eliminate candidates from the inequalities, then use the complete algorithm to eliminate the remaining candidates. VI. Simple Inequality Balancing [QX01+5] This technique is more of an art than a streamlined process, and it takes some getting used to. The easiest aspect of inequality balancing is eliminating the lowest or highest digit based on the direction of the inequality sign. First, inspect a square that lies in an inequality cage. If that square is "less than" another square, then the highest digit can be eliminated as a candidate from that square, since the highest digit cannot possibly be less than another digit. Similarly, if a square is "more than" another square, then the lowest digit (which is always 1) can be eliminated as a candidate from that square, since the lowest digit cannot possible be more than another digit. If a square is both "more than" and "less than" in relation to two or more squares, then both the highest and lowest digit can be eliminated immediately from that square. This is the easiest case, since you are not required to think about the direction of the inequality sign at all. Once the highest and lowest digits have been eliminated, it is possible to reduce the number of candidates further. Begin by comparing any two squares that have the same digit for either their lowest candidate or their highest candidate (or both). When two inequality squares have the same lowest candidate, that candidate can be removed from the square that is "more than" the other. Similarly, when two inequality squares have the same highest candidate, that candidate can be removed from the square that is "less than" the other. This technique can be applied to all inequality squares until no two have the same lower and upper candidates. Since this can be confusing to think about, I will illustrate it with an example. +============+============+============+============+============+============+ | | A | | B | | C | +============+============+============+============+============+============+ | 1 | 1234 | < | 1234 | > | 1234 | +============+------------+------------+------------+------------+------------+ | | /\ | | \/ | | /\ | +============+------------+------------+------------+------------+------------+ | 2 | 1234 | < | 1234 | < | 1234 | +============+------------+------------+------------+------------+------------+ We begin by eliminating lowest and highest candidates, in this case, 1s and 4s. Since A1 is less than B1 and A2, we eliminate 4 from A1. Since B1 is greater than A1, B2, and C1, we eliminate 1 from B1. Since C1 is less than B1 and C2, we eliminate 4 from C1. Since A2 is less than B2 and greater than A1, we eliminate 1 and 4 from A2. Since B2 is less than C2 and greater than A2, we eliminate 1 and 4 from B2. Since C2 is greater than C1 and B2, we eliminate 1 from C2. +============+============+============+============+============+============+ | | A | | B | | C | +============+============+============+============+============+============+ | 1 | 123 | < | 234 | > | 123 | +============+------------+------------+------------+------------+------------+ | | /\ | | \/ | | /\ | +============+------------+------------+------------+------------+------------+ | 2 | 23 | < | 23 | < | 234 | +============+------------+------------+------------+------------+------------+ Now we compare squares to their neighbors. A1 and A2 have the same highest candidate, 3. We eliminate 3 from the smaller square, A1. B1 and B2 have the same smallest candidate, 2. We eliminate 2 from the larger square, B1. A2 and B2 have the same smallest candidate, 2. We eliminate 2 from the larger square, B2. +============+============+============+============+============+============+ | | A | | B | | C | +============+============+============+============+============+============+ | 1 | 12 | < | 34 | > | 123 | +============+------------+------------+------------+------------+------------+ | | /\ | | \/ | | /\ | +============+------------+------------+------------+------------+------------+ | 2 | 23 | < | 3 | < | 234 | +============+------------+------------+------------+------------+------------+ We have thus deduced a solution for B2, but we can still continue. A2 and B2 have the same highest candidate, 3. We eliminate 3 from the smallest square, A2. B1 and B2 have the same smallest candidate, 3. We eliminate 3 from the largest square, B1. +============+============+============+============+============+============+ | | A | | B | | C | +============+============+============+============+============+============+ | 1 | 12 | < | 4 | > | 123 | +============+------------+------------+------------+------------+------------+ | | /\ | | \/ | | /\ | +============+------------+------------+------------+------------+------------+ | 2 | 2 | < | 3 | < | 234 | +============+------------+------------+------------+------------+------------+ We have now solved A2 and B1! Note that we could have just as easily inspected A2 and B2 to see that the only number less than 3 in A2 is 2, so 2 must be the solution. This brings me to the final point about inequality balancing, and the reason why I called it an art earilier. You will easily see by inspecting A1 and A2 that A1 must be 1. You will also have arrived at this result by comparing their highest candidate, 2. However, you can also see by inspection that C2 must be 4, even though the lowest/highest candidate method would not have yielded that result! +============+============+============+============+============+============+ | | A | | B | | C | +============+============+============+============+============+============+ | 1 | 1 | < | 4 | > | 123 | +============+------------+------------+------------+------------+------------+ | | /\ | | \/ | | /\ | +============+------------+------------+------------+------------+------------+ | 2 | 2 | < | 3 | < | 4 | +============+------------+------------+------------+------------+------------+ That is to say, the highest/lowest candidate method is not a complete general solution, as sometimes it fails to take into account candidates that are highest or lower than the possibility threshold. The supplement to the method to make it complete is either to inspect squares after you are done to see if anything can be logically eliminated, or to use the complete inequality balancing algorithm detailed above. In any case, this method should get you far enough that the number of squares that you need to manually inspect is relatively small. Note that in the example, C1 cannot be completely solved based on the given information. We can eliminate 1 as a potential candidate since 1 appears in the same row (block A1), but we cannot know whether the solution is 2 or 3 without more information. =============================================================================== B. Puzzle Variations [QX02] =============================================================================== I. Foreword The game consists of six regions, each with seven locations. The puzzle size varies by region, and the puzzle type varies by location, with three difficulty levels per location. That being said, there are 6*7*3 = 126 different puzzle varieties (42 excluding difficulty levels), but there are essentially seven basic types, since the size of the puzzle only changes the overall difficulty of the puzzle, not the actual strategy required. The available regions are as follows. Ocean - 4x4 square grid Canyon - 5x5 square grid Forest - 6x6 square grid Mountain - 7x7 square grid Sky - 8x8 square grid Beyond - 9x9 square grid II. Basic Board a) Ocean: Beginnings N= The solution to the square is N. Equality cages can only be one square wide. N+ All digits in the cage must add to N. b) Ocean: Ocean Floor Even The digits in the cage must be even digits (2468). A particular digit can appear more than once in a single Even cage, as long as it does not violate the rule of appearing only once in a column or row. Odd The digits in the cage must be odd digits (13579). A particular digit can appear more than once in a single Odd cage, as long as it does not violate the rule of appearing only once in a column or row. c) Ocean: Shipwreck N- The digits in the cage must subtract to N. A Subtraction cage always consists of two squares, and the lower digit is always subtracted from the higher digit (square order does not matter). d) Ocean: Kelp Nx The digits in the cage must multiply to N. e) Ocean: Shelf N% The digits in the cage must divide to N. A Divison cage always consists of two squares, and the smaller digit always divides the larger digit (square order does not matter). f) Ocean: Arch <,> The digits in the cage must be less than or more than their neighbors, according to the position of the sign. AB means "A more than B" or "B less than A". g) Ocean: Shallows Paint The location of the cages is only partially defined. The solver must deduce the location of the cages by thinking about partial solutions to the cages. Some tips to figuring out where to paint in the cages are as follows. -A black border on a cage indicates that the cage does not extend in that direction. -Inequality cages extend through all inequality signs, and no further. -Subtraction and division cages contain only two squares. -All other cages except Even and Odd cages must contain at least two squares. -A cage must contain at least as many cages as the smallest possible equation suggests. -An unpainted square that is inaccessible by all cages except one must necessarily be part of that one cage. -An ambiguous square need not be painted in. The puzzle can be solved without painting in all the cages. h) Canyon: Shore Empty Cage Empty Cages have no rules assigned to them. The only way to deduce solutions to empty cages is through column/row elimination. i) Canyon: Grotto Straight All digits in a Straight cage must differ from each other by 1 (square order does not matter). For example, possible straight cage combinations could be 123, 765, 2345, or 15342. j) Canyon: Cave Double Board You are to solve two boards with identical solutions, but differing cages. Eliminating candidates and choosing solutions for one board automatically does the same for the other board. =============================================================================== C. Introductory Walkthrough [QX03] =============================================================================== I. Ocean: Beginnings: Puzzle #1 +==============+==============+==============+==============+===============+ | | A | B | C | D | +==============+==============+==============+==============+===============+ | 1 | 7+ [1234] | 7+ [1234] | 1= [1234] | 2= [1234] | +==============+--------------+--------------+--------------+---------------+ | 2 | 2= [1234] | 5+ [1234] | 7+ [1234] | 3= [1234] | +==============+--------------+--------------+--------------+---------------+ | 3 | 3= [1234] | 5+ [1234] | 7+ [1234] | 7+ [1234] | +==============+--------------+--------------+--------------+---------------+ | 4 | 3+ [1234] | 3+ [1234] | ~7+ [1234] | ~7+ [1234] | +==============+--------------+--------------+--------------+---------------+ The tilde (~) indicates that the 7+ cage on the bottom is different from the 7+ cage above it. The first step in any puzzle is to fill in the equality cages, if they exist. Filling them in and then eliminating the solution from all candidates in the same row and column yields: +==============+==============+==============+==============+===============+ | | A | B | C | D | +==============+==============+==============+==============+===============+ | 1 | 7+ [4] | 7+ [34] | 1= 1 | 2= 2 | +==============+--------------+--------------+--------------+---------------+ | 2 | 2= 2 | 5+ [14] | 7+ [4] | 3= 3 | +==============+--------------+--------------+--------------+---------------+ | 3 | 3= 3 | 5+ [124] | 7+ [24] | 7+ [14] | +==============+--------------+--------------+--------------+---------------+ | 4 | 3+ [14] | 3+ [1234] | ~7+ [234] | ~7+ [14] | +==============+--------------+--------------+--------------+---------------+ Inspecting A1, we see that the solution is 4. By eliminating 4 from column A and row 1, we get B1 = 3 and A4 = 1. Note that this solves the 7+ cage automatically (as 3+4=7). Inspecting C2, we see that the solution is 4. By eliminating 4 from column C and row 2, we get B2 = 1 and C4 = 2. +==============+==============+==============+==============+===============+ | | A | B | C | D | +==============+==============+==============+==============+===============+ | 1 | 7+#4 | 7+#3 | 1= 1 | 2= 2 | +==============+--------------+--------------+--------------+---------------+ | 2 | 2= 2 | 5+ [1] | 7+ 4 | 3= 3 | +==============+--------------+--------------+--------------+---------------+ | 3 | 3= 3 | 5+ [14] | 7+ 2 | 7+ [14] | +==============+--------------+--------------+--------------+---------------+ | 4 | 3+ 1 | 3+ [24] | ~7+ [3] | ~7+ [4] | +==============+--------------+--------------+--------------+---------------+ The pound (#) indicates that the 7+ cage has been fully solved. I decided not to use # to indicate completed equality cages for simplicity. By inspecting B2, we see that the solution is 1. By eliminating 1 from column B and row 3, we get B3 = 4 and D3 = 1. By eliminating 4 from column B, we get B4 = 2. By inspection, we also see that C4 = 3 and D4 = 4. Note that the conditions of the addition cages are automatically satisfied by the placement of the numbers. +==============+==============+==============+==============+===============+ | | A | B | C | D | +==============+==============+==============+==============+===============+ | 1 | 7+#4 | 7+#3 | 1= 1 | 2= 2 | +==============+--------------+--------------+--------------+---------------+ | 2 | 2= 2 | 5+#1 | 7+#4 | 3=#3 | +==============+--------------+--------------+--------------+---------------+ | 3 | 3= 3 | 5+#4 | 7+#2 | 7+#1 | +==============+--------------+--------------+--------------+---------------+ | 4 | 3+#1 | 3+#2 | ~7+#3 | ~7+#4 | +==============+--------------+--------------+--------------+---------------+ With the minimum sixteen moves, the puzzle has thus been solved. Note that it was not necessary to consider the rules of the addition cages at all, since the puzzle was easily solved by simply row/column elimination. We could have used the addition cages to solve some of the squares if we desired it, however. =============================================================================== D. Closing Comments [QX04] =============================================================================== Everyday Genius: Square Logic is fascinating to me because it contains over 20,000 puzzles, and the developer asserts that every puzzle can be solved without guessing. They can get insanely tricky, but so far I haven't run into a puzzle where I needed to guess at an answer. I'm certain that you can construct a puzzle within the Square Logic framework that WOULD be unsolvable without guessing, but as to whether the existing puzzles in the game are all solvable remains to be seen. I'm willing to put my faith in the system, though, since if the developers could code a way to generate thousands of unique varieties of these puzzles, I'm sure they could also handle making it so they're solvable. I think the intrigue of the game is not completing a puzzle, but rather, completing it correctly. At any point in the game you can make guesses and figure out the solution, but since completing the puzzle yields jack squat, there's no incentive too. Rather, I'll be stumped at a juncture, thinking, "now how am I supposed to figure out that this square should be this value? There has to be a way..." and the fun part is figuring out that way. Seeing as I could spend a good twenty minutes on the 9x9 puzzles, I can't help but think that the 20,000 included puzzles are excessive. I certainly won't finish them all in my lifetime, nor will I probably want to. But I'm sure it will please the puzzle fanatics out there to know that they can play this game for a long time before they end up repeating puzzles. A really long time. The first version of the game has some issues with recordkeeping and other issues in general. You have the option of resetting all the puzzles for a location or region, but why you would want to, I have no idea, unless you felt the 5200 puzzles in the region went by too fast and wanted a repeat or something. The worst part of the game, and the part that needs to be fixed IMMEDIATELY, is the advancement. There are 42 hotspots in the game, 7 per region, and each one starts you on puzzle #1. You can play puzzles #1-#12 if you like, but most likely you'll want to play the challenge puzzle (#13) so you can unlock the other 787 puzzles (487 for double board locations) and continue to the next hotspot. The problem is that beating the challenge puzzle then makes puzzles #1-13 unplayable unless you reset the location, and resetting the location means your completion progress for any of the puzzles in that location is reset. Why not just add puzzles #1-13 to the list of playable puzzles, instead of starting at #14? And some of the records are just bunk, because your record for puzzles completed in a region counts replayed puzzles, so you can replay one puzzle hundreds of times and increase the counter (why on earth you'd want to do so notwithstanding). The thing that really makes me sad about this is not that you can get the counter up as high as you like, but this: if I did happen to play all the puzzles in a region, I'd like my stats counter to be a nice, round number equal to the total number of puzzles in that region. But since I jumped straight to the challenge puzzle my first run through, I'd have to reset the location just to play the first twelve puzzles I missed, and... why do I even have to think about this? It wouldn't be a problem if the resetting issue was fixed. And your "rank" is set to whatever challenge puzzle you last completed regardless of how far you've gotten, although whether anybody cares about your rank is another issue. I'll try in future versions to detail some more important aspects of the game. For now, I just wanted to get my inequality balancing algorithm published, since large inequality cages can be a turn-off if you don't understand a basic way of solving them. I have some ideas, so look forward to them if you're interested in the game and in this guide, otherwise, I hope you found this at least a tad helpful. Cheers! =============================================================================== E. Contact Information [QX05] =============================================================================== You may email me at Sheepdude@gmail.com. Everday Genius: Square Logic and all related trademarks are property of the game developer, Mumbo Jumbo, and their respective owners. Submitted for publishing only on www.gamefaqs.com. Copyright 2009 Brandon Williams ===============================================================================