# GeekDad Puzzle of the Week: Cross Number Fail – Solution

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There’s a problem with this week’s puzzle. The grid lays out as follows:

Across
1-2-3: The first digit is less than the second digit by the same amount as the second digit is less than the third.
4-5-6: (Reversed) A square.
7-8-9: The square of an odd number.

Down
1-4-7: A factor of 2-5-8.
2-5-8: Odd.
6-9: A cube.

One clue is incorrect. Which one is it? Fill in the digits in each box of the grid. (There are no 0′s.)

SOLUTION

7-8-9 is the incorrect clue. Your grid should fill in as follows:

It is impossible to fill in anything until you determine the incorrect clue.

6-9 can only be 27 or 64. But 7-8-9 cannot end in 4 since it is the square of an odd number, and it cannot end in 7 since no square ends in 7. Therefore either 6-9 or 7-8-9 is wrong.

2-5-8 is odd, so 8 is an odd digit. No three figure square of an odd number has an odd digit for its second digit so either 2-5-8 or 7-8-9 is wrong. Only one clue is wrong so 7-8-9 is the incorrect clue. All other clues work out correctly if so.

6-5-4 must be a square starting with a 2 or 6. It must be 225, 256, 289, 625, or 676.

Since 2-5-8 is odd, 1-4-7 is odd and 2-5-8 must be 1-4-7 multiplied by an odd number (3 or 5, but no more because of 1-2-3).

4-5-6 is 522, 652, 982, 526, or 676. Bear in mind that 2-5-8 is three or five times 1-4-7. If 4 and 5 is 52, then we must have –5–x 3 producing –2– (not –5–x 5 as this would make 2 at least 7 and 3 would not be less than 10). But –5– x 3 cannot produce –2– so 522 and 526 are not possible.

If 4 and 5 is 65, then we have –6– x 3 =  –5– (impossible). If 67, then we have –6– x 3 =  –7– (impossible). If 98, then –9– x 3 =  –8– (which is the only possibility). Since that is the only possibility, 4-5-6 must be 982 and 6-9 is 27.

1 must be 1 and 2-5-8 must be 3 times 1-4-7. If five times 3, it would be more than 9, so 2 must be 5 and 3 is 9.

2-5-8
is odd and divisible by three, so 585 is the only possibility. 1-4-7 is therefore 195.

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