GeekDad Puzzle of the Week: Cross Number Beta – Solution

Congratulations to Judd Schorr for being this week’s selection from a large batch of correct answers. Judd gets to shop for all sorts of Halloween goodies with a $50 gift code to ThinkGeek!
Thanks to all who submitted answers. Check the solution for your code for $10 off your next $30 ThinkGeek purchase. Solution after the jump.

Special thanks to ThinkGeek for providing our prizes!

ACROSS
1. Only two different digits are used in this odd number.
5. A perfect cube.
6. A prime number.
8. The same when reversed.
11. The first digit is the sum of the digits of 8 across.
12. A prime number multiplied by two, and a prime number when reversed.
13. A perfect cube

DOWN
1. The sum of the digits is a prime number which is greater than 19.
2. A prime number, and twice a prime number when reversed.
3. A multiple of the number formed by the last two digits of 4 down.
4. Each digit is less than the preceding one.
7. A multiple of one-third of 8 across.
9. A multiple of the cube root of 13 across.
10. Four times the sum of its digits.

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Solution

10 down could be 12, 24, 36, or 48. 13 across could start with 1, 2, 3, 5, 7. The only one of these which can be the second figure of 10 down is 2, therefore 10 down is 12, and 13 across is 216.

8 across must start with a 1

Consider 7 down with 8 across. One-third of 8 across must end in 7, and must be 37, 47, or 57 ending in 6, and starting with an odd digit (since 6 across is a prime number). A little work will show that it can only be 8 x 47 (376), and 8 across must be 3 x 47 = 141.

Therefore the first digit of 11 across is 6

The first three digits of 4 down must be 9, 8, 7.

In 5 across, the only four-figure perfect cube ending in 8 is the cube of 12 (1,728).

2 down must start with an even digit (twice a prime number when reversed). 72, 76, 78 are not twice a prime number, but 74 is.

2 down is therefore 47.

9 down must be 42 or 48. If it’s 42, 12 across would have to be 32 or 92 (a prime number when reversed), but neither of these is twice a prime number, therefore 9 down is 48 and 12 across can only be 38.

In 1 down, the least prime number greater than 19 is 23. The two missing digits in 1 down would then be 9 and 9.

Since 1 across is odd, it must end in 9.

3 down must be 42… or 92… (see 1 across). 92… cannot be a multiple of 61, but 427 is.

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