Figure Logic

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Figure Logic

figure logic

Figure Logic is the name for a puzzle in Dell Puzzle magazines. Here is one that I made up. As you can see, it looks much like a crossword puzzle. And solving it is much like solving a crossword puzzle. There are numbered clues, and you can deduce interrelationships between the numbers. When solved, each little square will contain a one digit number. None of the multiple digit numbers (like 1-across) begins with a zero. The same digit may occur more than once in a multiple digit number.

The numbered clues limit the various numbers. For example, a two digit number that is 40 greater than another two digit number must be between 50 and 99. And the intersecting numbers limit each other. For example, if 15A (in the diagram) happened to be between 25 and 33, then 15D would be between 20 and 39. Or if 13A happened to be divisible by 5, then it must end in 5, because 14D cannot begin with 0.

Clues:

Across:

1. 11-across squared.
4. 3 more than 14-down.
5. 2 times 15-across.
7. 12-down + 5-across.
9. 2-down - 15-across.
10. 5 more than 9-across.
11. 10 less than 8-down.
13. 1-down + 3-down.
15. 1/2 of 5-across.
16. 4-down - 1-across.

Down:

1. 13-across - 3-down.
2. 11-across + 3-down.
3. 30 more than 5-across.
4. 2-down squared.
6. 1-across - 16-across.
7. 10-across rearranged.
8. 3 times 4-across.
12. 2 times 4-across.
14. 20 more than 3-down.
15. 3 more than 15-across.

Click here for the answer.

Addendum:

Here is another figure logic that I designed:

small figure logic

Across:

1. 8D + 3x6A.
3. 2D + 10.
4. 8D + 1.
6. 3 x 1D.
8. 2D + 2.
9. 3A x 1D + 1.

Down:

1. 4A - 2.
2. 8D - 1.
3. 9A - 4A - 6.
5. (4A+4) x (3A-2).
7. 2D + 3A.
8. 1D + 1.

Click here for the answer.

Addendum:

All puzzle composers make mistakes, on occasion. Over the years, two Dell figure logic puzzles have had a clue like this: "The product of the digits is 2-Down," when one of the digits was zero, and the zero was ignored when forming the product. Twice the clue was "Consecutive digits," which I have learned to be careful of. It could mean "Consecutive digits in either ascending or descending order," but may mean ". . . in any order," which is not an error, just a natural ambiguity which I didn't anticipate. In the March 2003 Math Puzzles and Logic Problems, figure logic #12 has two solutions, if 0 is a multiple of 2. I am sure that many people would not consider 0 or 2 to be multiples of 2. Looking up "multiple" at MathWorld's site, I see that 0 is a multiple of 2 (I was unsure): "A multiple of a number x is any quantity y = nx with n an integer."

Also, over the years, Dell seems to have been unsure if their readers know what these words mean (sometimes defining them, and sometimes not): prime, square, square root, cube, cube root. As a writer, I sympathize; it is a bother to define your terms every time.

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