# Think Tank

by K.H. “Wicks” Wickremasinghe

Little David went to the post office to buy stamps for his father. When he reached the counter, he had forgotten what his father wanted. From what he remembered, he asked the clerk for some 1-cent stamps; six times as many 5-cent stamps and 25-cent stamps for the remainder of the \$4.00 his father had given him. The clerk who was a student engineer had no difficulty in figuring out what David wanted.

How many of each kind did David get?

Grand Prize Winners
Congratulations to Robert Szewc of MY'TE Products Inc. (Indianapolis, Ind.) for solving the Floor Tiles Challenge, and to Peter Douglas of Custom Chip Connections Inc. (Hunstville, Ala.) for solving CrossNumber 75!

CrossNumber 77
(All answers are numbers; prime means a prime number.)

In this variation of the CrossNumber, rather than running numbers across and down, the answers will appear diagonally. Left to right will be referred to as “left,” and right to left will be referred to as “right.” No number appears twice and none begins with zero.

Left to Right
1. 8 Right squared
2. 16 Right + 2 x 12 Left
3. 14 Right squared
4. 14 Right x 19 Right
6. 14 Right x 12 Left
9. 26 Right + 4 x 14 Right
11. Prime
12. Prime
15. 17 Left x 18 Left/3
17. 18 Left + 2 x 14 Right
18. Prime
20. 11 Left x 18 Left
21. 11 Left + 13 Right + 26 Right
22. 1 Left – 2 x 21 Left
23. Prime
25. Prime

Right to Left
2. (1 Left + 2 Left)/2
4. Prime
5. 18 Left squared
6. 8 Right x 13 Right
7. 11 Left squared
8. (11 Left + 18 Left)/2
10. 6 Left + 2 x 18 Left
13. (14 Right + 17 Left)/2
14. Prime
16. 7 Right + 2 x 8 Right
19. Prime
21. Prime
23. 1 Left + 21 Left – 8 Right
24. 16 Right + 21 Left + 3 Left
25. 8 Right x 11 Left
26. 8 Right + 12 Left + 13 Right

Solutions to July's Puzzles:

CrossNumber 75

Floor Tiles
Answer: 13' a side. A total of 49 black tiles and 120 white tiles.

Solution: Let B and W represent the black and white tiles, and n2 the area of the patio. Let p be the length of the black-sided squares that Tom planned. Let the side of the white squares that Doris planned be q = p + 4.

W = q2 – 1 = (p + 4)2 – 1; B = p2; W + B = n2; n2 = p2 + 8p + 15 p2; let x = p + 2.

Then n2 – 2x2 = 7. For n between 10 and 20, only n = 13 will give an integer value of x. Therefore, W = 120 and B = 49.

Contest Rules: All entries must be received by September 30, 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.

online
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