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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.)*

Download the grid here.

**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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