Think Tank
08/01/2002
by K.H. "Wicks" Wickremasinghe
The Building Lot
"What is the size of the lot you bought to build your starter home?" Susan asked David, the newly hired engineer.
David replied, "It is a rectangular lot where the diagonals plus its longer sides are nine times the length of one of the shorter sides. All of the lengths are an integral number of feet."
What is the smallest possible dimension of the lot?
Grand Prize Winners
Congratulations to Ivy Qin of Kulicke & Soffa Industries (Willow Grove, Pa.) for solving the Dwindling Society challenge, and to Albert Jew of Raytheon Co. (Attleboro, Mass.) for solving CrossNumber 74!
CrossNumber 76
(All answers are numbers; prime means a prime number.)
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Across
1. 2 x (27 Down + 13 Down)
4. (4 Down squared)/4
7. 4 Across x 8 Down
9. Prime
10. 3 x 4 Down
14. 4 Down x 29 Down/2
17. 11 Down x (4 Down + 27 Down)
18. 4 Down x (3 Down - 21 Down)
19. 1 Down x (27 Down - 8 Down)
23. 26 Down x (4 Down - 6 Down)
26. 12 Down x 27 Down/2
28. 2 x 8 Down x (14 Across - 30 Down)
31. 2 x 4 Down x 8 Down
32. 3 Down + 12 Down
Down
1. Prime
2. 8 Down x (4 Down + 27 Down)
3. Prime
4. 27 Down + 2 x 8 Down
5. 4 Down + 8 Down x 21 Down
6. Prime
8. Prime
9. (18 Across + 32 Across)/2
11. (6 Down + 8 Down)/2
12. Prime
13. 2 x (10 Across + 6 Down)
15. 3 Down x 8 Down
16. 19 Across - 4 Down
20. 15 Down - 3 Down - 11 Down
21. (24 Down + 26 Down)/2
22. 4 Down x 6 Down/2
24. 8 Down x 27 Down/2
25. 14 Across + 3 Down
26. 6 Down + 8 Down
27. 20 Down/(21 Down - 6 Down)
29. Prime
30. (27 Down squared)/4
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Solutions to June's Puzzles:
CrossNumber 74
Dwindling Society
Answer: 240
Solution: Let the number of members in the first year be X. At the beginning of the second year, there were 9/10 X members. During the second year, the society lost 2/3 of 1/10 X = 1/15 X. Total lost at the end of the second year was = X/6. All that remained was 5/6 X. Similar working would show that at the end of the seventh year, there were 3/16 X members. Thus, X = 240.
Contest Rules: All entries must be received by August 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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