# Think TANK

by K.H. “Wicks” Wickremasinghe

Floor Tiles

Tom bought black and white tiles, 12 x 12-inches each, to lay on his square patio deck. He planned to have a perfect square of black tiles in the center of the deck with a border of white tiles around it. But his wife Doris, a design engineer, wanted one black tile in the center surrounded by white tiles to form a perfect square and a border of black tiles.

“Oh, no. I don't want to go back to the store to change them,” Tom said.

“You don't have to,” replied Doris. “Because the patio is less than 20 feet and more than 10 feet a side, we can increase the size of the white square by 4 feet more than the black square you planned. We still need the same number of tiles.”

What was the size of the patio, and how many black and white tiles did they use?

Grand Prize Winners
Congratulations to Martin Mucciarone of Pyxis Corp. (San Diego, Calif.) for solving the 1,001 Nights Challenge, and to Fred Strobl of Central Steel & Wire Co. (Chicago, Ill.) for solving Cross Number 73!

CrossNumber 75

Across
1. 2 x 21 Down / 28 Across
2. 14 Down + 29 Across
4. 1 Across + 31 Across
6. 29 Across + 31 Across
7. 19 Across + 23 Across
9. 4 Across squared
11. 1 Across + 9 Across
13. 19 Across – 1 Across
15. 17 Across – 7 Across
16. 1 Across + 29 Across
17. 4 Across + 29 Across
18. 25 Across + 29 Across
19. 28 Across – 4 Across
21. 18 Across – 1 Across
23. 1 Across + 25 Across
25. Square root of 22 Down
27. 4 Across + 31 Across
28. 13 Across + 29 Across
29. 1 Across + 4 Across
30. 5 Down – 1 Down
31. 18 Across / 3

Down
1. 4 Across + 2 Down
2. 1 Across + 17 Across
3. 1 Across x 4 Across
5. 3 Down – 17 Across
6. 22 Down + 26 Down
8. 15 Across x 25 Across / 2
10. 1 Across squared + 6 Down
12. 4 Across x 16 Across
14. 27 Across + 31 Across
20. 27 Across + 1 Down
21. 1 Down + 22 Down
22. 27 Across + 30 Across
24. 31 Across + 2 Down
25. 2 Down + 24 Down
26. 6 Across + 20 Down

Solutions to May's Puzzles: CrossNumber 73

1,001 Nights

Solution: Let A, B and C represent the number of nights that there were dancers, musicians, and jugglers.
Equation 1: A + B + C = 1,001
Equation 2: B2 = A x C
Let B/A = C/B = X, then B = XA and C = BX = X2 A

Substituting in Equation 1 is A + XA + X2 A = 1,001. A (X2 + X + 1) = 1,001. The only factors of 1,001 are 7, 11 and 13.
Therefore, A (X2 + X + 1) = 7 x 143 or 11 x 91 or 13 x 77.

Case 1. If A = 7, then (X2 + X + 1) = 143; no feasible solution.
Case 2. If A = 143, then (X2 + X + 1) = 7; X = 2 and B = 286, which is greater than 100.
Case 3. If A = 11, then X2 + X – 90 = 0; X= 9, and B = 99.
Case 4. If A = 91, then X2 + X – 10 = 0; no integer solution.
Case 5. If A = 13, then X2 + X – 76 = 0; no integer solution.
Case 6. If A = 77, then X2 + X – 12 = 0; X = 3 and B = 231, which is greater than 100.

Contest Rules: All entries must be received by July 31, 2002. The winners of the word puzzle and CrossNumber (can be the same person) will be drawn from all correct entries. Fax all entries to 847-634-4240. All entries must include name, complete address, company affiliation and daytime phone number to be considered.