Squares Within Squares
04/01/2002
by K.H. "Wicks" Wickremasinghe
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Squares Within Squares
Mary wanted to plant tulips and marked out a 12 feet square area with four stakes at the corners, intending to prepare the bed later in the week. Her husband, Joe, wanted to plant roses, and not seeing Mary's stakes, marked a 15 feet square bed with four stakes at the corners. When both went out to the garden a few days later at the same time, they found that Joe had placed one of his stakes at the exact center of Mary's intended bed, as shown in the dia gram. The distance BE was 3 ft.
They compromised and decided to plant petunias in the common area, shown as shaded in the diagram.
What is the area of the petunia bed?
Grand Prize Winners
Congratulations to Guy D. Couturier of MultiChip Integration Branch U.S. Air Force (Wright-Patterson AFB, Ohio) for solving "The Street Where They Live Challenge", and to Dr. Hao Tang of Loctite (Rocky Hill, Conn.) for solving Cross Number 70!
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CrossNumber 72
In this CrossNumber, no answer is prime, but except 21 Across, each is the product of two different primes. 21 Across is the product of three different prime numbers.
Across
1. 4 x 27 Across - 1
4. 18 Down + 4 x 10 Across
7. 29 Down + 31 Down
8. 3 x 6 Down + 1
10. See 6 Down
11. 3 x 25 Across - 10 Across
13. 8 Down + 25 Across - 1
16. (3 Down + 15 Down) x (1 Down + 25 Across - 31 Down)
19. 26 Down + 27 Across
20. [10 Across x (10 Across + 30 Across)] / 2
21. (7 Across + 4 Across) x (3 Down + 29 Down)
24. 6 x 27 Down - 10 Across
25. 27 Across + 31 Down - 30 Across
27. See 25 Across
28. 20 Across + 4 x 30 Across
30. See 25 Across
32. 5 x 7 Across - 2
33. 6 Down + 27 Down + 31 Down
Down
1. See 27 Down
2. 3 x 33 Across + 2
3. See 27 Down
5. 6 Down + 33 Across
6. 2 x 10 Across + 29 Down
8. 3 x 7 Across + 10 Across
9. 13 Across + 26 Down - 3
12. (27 Across + 29 Down) x (2 x 25 Across - 7 Across)
14. (3 Down + 29 Down) x (18 Down - 24 Down)
15. 7 x 25 Across - 1 Down
17. 1 Down + 19 Across + 29 Down
18. 17 Down + 30 Across
22. 2 x 33 Across + 25 Across
23. 17 Down + 25 Across - 1
24. 10 x 31 Down - 30 Across
26. 20 Across - 10 x 10 Across
27. 1 Down + 3 Down
29. See 6 Down
31. See 7 Across
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Solutions to February's Puzzles:
Cross Number 70
The Street Where They Live
Answer: Liz's is 114 and Brenda's is 65.
Solution: As the difference of the numbers is 4, the well-known formula for a sum of an arithmetic series reduces to s = n [a + 2(n - 1)]. Obviously, Liz has an even number and Brenda an odd number.
2926 = 11 x 266; 22 x 133; 19 x 154 or 38 x 77.
If n = 11 then a = 246; if n = 22 then a = 89 (odd and inadmissible); if n = 19 then a = 118; if n = 38, a = 3 (odd and inadmissible). Then the number of the last house is 286 or 190.
Solving for Brenda, 3999 = 31 x 129 or 43 x 93. This gives us a = 69 or 9. The number of the last house is 189 or 177.
Only when n = 3 is the last number 189.
Contest Rules: All entries must be received by April 29, 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.