Draw up a list of squares. Pay attention to digits in common between a number and its square.
If a clue requires “one-third of entry X,” then you know X is evenly divisible by 3 (and so on).
Answers cannot be zero, or begin with a zero.
Answers cannot be negative. If your final answer is “X minus Y”, then you know X is larger than Y. But “taking the difference” between two numbers means use the absolute value (omit the sign).
In the Blue table, clue 8-C says this entry is the square root of 1-B. Thus 1-B equals 8-C squared. The grid indicates 8-C has two digits, while 1-B has four. These values cross in the grid, sharing a digit; mark the options on your list of squares. In the Green table, to prevent 4-B from being zero, the product of the digits in 1-B must be non-zero; it can only be 6724 (= 822).
The Figure Logic puzzle on this page has a grid composed of three small cubes. Each cube shows eighteen squares on the visible faces. Your goal is to fill each square with a digit from 0 through 9, though a zero will never begin an answer. The three separate cubes are referred to by their color: red, green, or blue.
Within each cube, you'll be solving in three dimensions as indicated by the arrows: (A) goes down to the left; (B) goes down to the right; (C) goes across from the lower left to the right. Work back and forth among the three cubes to complete the puzzle.
Clue Format: The tables below contain all the clues you need. An entry such as 2-A means find the Blue Cube, find square 2 on it, and move in direction A.
Solving on Paper: To obtain a large grid with plenty of working space, click on the diagram titled Cubism below. This takes you to an image printable in landscape (sideways) orientation.
Puzzle Version: A standard 3D figure logic puzzle uses a single large cube. The puzzle on this page is unique – it uses multiple cubes, which makes the designation of clues more complex. We experimented with the puzzle style, creating two color versions, plus a black-and-white version adapted for monochrome printers. All versions are identical except for how the clues are written. Select whichever works best for you:
|2-A||2-A minus 8-C|
|3-A||Square of 7-C|
|6-A||One plus the average of two different 4-B entries|
|9-A||Average of two different 2-A entries|
|1-B||5-B times the average of 9-A and 9-C|
|4-B||Difference between 9-C and twice 2-A|
|5-B||Its square is found on one of the cubes|
|10-B||8-C plus the average of two different 9-A entries|
|7-C||Average of 8-C and 6-A|
|8-C||9-A minus 10-B|
|9-C||An odd number|
|11-C||Square of the difference between 6-A and 10-B|
|2-A||Difference between two 5-B entries|
|3-A||Difference between two 11-C entries|
|6-A||An odd number|
|9-A||6-A plus one-third of 2-A|
|1-B||7-C times the difference between 3-A and 11-C|
|4-B||First digit of 3-A divided into the product of the digits in 1-B|
|5-B||Product of its digits equals 8-C|
|10-B||One-fifth of the difference between 3-A and 1-B|
|7-C||10-B minus 9-C plus 7-C|
|8-C||Average between 5-B and the average of two different 8-C entries|
|9-C||Two more than 9-A|
|11-C||Square of 4-B|
|2-A||6-A minus 7-C|
|3-A||2-A plus the square of one less than 6-A|
|6-A||8-C plus one-third of 9-A|
|9-A||A 10-B entry plus the average of two different 9-A entries|
|1-B||1-B plus 11-C|
|4-B||An even number|
|5-B||Average of 6-A, 5-B, and 2-A|
|10-B||Average of two different 7-C entries|
|7-C||One plus one-third of 2-A|
|8-C||Square root of 1-B|
|9-C||A whole multiple of 7-C|
|11-C||Sum of its digits equals 8-C|
Tuum Est - It Is Up To You
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