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Figure Logic Puzzle

Figure Logic:  Cubism / Solving Hint

General Solving Tips

A table of squares is useful. 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).

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 (that is, omit the sign of the result).

Starting Hint for Puzzle on this Page

On the Blue Cube, 1-B equals 8-C squared. On the same Cube, the product of the digits in 1-B is non-zero (see clue 4-B). Thus on the Blue Cube, 1-B can only be 6724 (= 822).

This Figure Logic puzzle uses three small cubic grids.  Each grid square is to be filled in 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 entry 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 anywhere on the colored cubes below; this takes you to an image which you can print in landscape (sideways) orientation.

Puzzle Version: A 3D figure logic puzzle typically uses a single large cube.  The puzzle on this page uses multiple cubes, which makes clue designation more complex.  As an experiment, two color versions of the puzzle were developed.  There is also 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

Copyright © 2008-2018 Georgena Sil. All Rights Reserved.