Think Tank
06/01/2002
by K.H. "Wicks" Wickremasinghe
Dwindling Society
The Math and Logic Teasers Association (MALTA) was inaugurated a few years ago. At the end of the first year, its membership dropped by 10 percent. At the end of the second year, the group lost two-thirds of the number of members lost the previous year. The third year, it lost 10 percent of the remaining members, and at the end of the fourth year, it lost two-thirds of the members lost so far. This loss continued in a similar alternating manner until the end of the seventh year when only 45 members remained.
How many members were there in the first year?
Grand Prize Winners
Congratulations to Zalman Liss of Lutron Electronics (Coopersburg, Pa.) for solving the Squares Within Squares Challenge and to John Davies of T.D. Systems (El Sobrante, Calif.) for solving CrossNumber 72!
CrossNumber 74
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Across
1. (7 Across / 2) squared
4. (10 Across + 29 Across) squared x 2
7. 10 Across + 29 Across + 27 Down
8. 5 Down x 10 Across / 2
10. Prime
11. 2 x 31 Across + 6 Down - 13 Across
13. (5 Down / 2) squared
15. 1 Across / 4
17. Root of (13 Across x 1 Down)
18. 3 x 24 Down
19. (5 Down + 29 Across) squared / 4
21. 29 Down x (5 Down - 1)
23. 30 Across + 31 Across
26. 3 x 5 Down / 2
28. 10 Across squared
29. 29 Down - 1
30. 4 x 27 Down squared
31. 13 Across x (5 Down - 10 Across)
Down
1. 5 Down squared
2. 2 x 27 Down / 3
3. Root of (1 Across x 15 Across)
4. 2 Down x 29 Down - 5 Down
5. 8 Across - 13 Across
6. 3 x 18 Across
9. 3 x 16 Down
11. 23 Across - 17 Across - 5 Down
12. 23 Across + 26 Across + 9 Down
14. 2 Down squared
16. 29 Down squared
19. 28 Across x 29 Across
20. (1 Across + 3 Down) / 2
22. 9 x 19 Across
24. 29 Across squared
25. 2 Down x 29 Across + 2 x 10 Across
27. 29 Across + 29 Down
29. Prime
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Solutions to April's Puzzles:
CrossNumber 72
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Squares Within Squares
Answer: 36 square feet
Solution: Extend EO to meet AD at H, and FO to meet AB at G. Draw the diagonals of the smaller square, AC and BD. Then it can be shown that triangles BOE and HOD are congruent. Triangles BGO and DOF are congruent. Then BGOE and DHOF are equal in area, and AGOH and EOFC are equal. The shaded area is one-quarter of the square.
Contest Rules: All entries must be received by June 28, 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.