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Puzzles by Tuum Est ˆ

Cubism / Figure Logic with 3-Cube Grid

Color Box Version

Cubism / Solving Tips and Starting Hint

General Solving Tips

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.

Subtraction vs. Difference

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).

Starting Hint for Puzzle on this Page

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:

Figure Logic Grid, Copyright Georgena Sil, Tuum Est

Clues:  Red Cube

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

Clues:  Green Cube

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

Clues:  Blue Cube

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

Georgena S. Sil
Saskatoon, Canada
Physicist & Technical Writer
Alumnus: University of British Columbia
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Copyright © 2008-2019 Georgena Sil. All Rights Reserved.