# Think Tank

by K.H. “Wicks” Wickremasinghe

The Street Where They Live
Liz and Brenda live on opposite sides of the street, where there are an equal number of houses on each side. The odd numbers start with 1 and the even numbers start with 2; both sides increase in steps of 4. The sum of numbers above Liz's house number on her side of the street total 2,926. The sum of the numbers above Brenda's house number on her side equal 3,999.
What are Liz and Brenda's house numbers?

Grand Prize Winners
Congratulations to Roman Gurevich of National Semiconductor (Moun-taintop, Pa.) for solving the Circular Park challenge, and to Brent Lybrand of Delphi Connection Systems (Landrum, S.C.) for solving Guest CrossNumber 1.

CrossNumber 70
Each answer is equal to the sum of two integral squares. In addition, each answer is also a prime (e.g., 5 [prime] equals the square of 1 plus the square of 2). No number begins with zero and none is repeated.

Across

1. 4 x 24 Across + 5 Across
3. 4 x 17 Down + 27 Across
5. 2 x 10 Across – 7 Down
6. 4 x 12 Across + 25 Across
8. 2 x 25 Across – 1 Across
10. 2 x 24 Across – 19 Across
11. 4 x 1 Across + 12 Across
12. 10 Across + 13 Down – 7 Down
15. 2 x 2 Down – 1 Down
16. 4 x 10 Across + 19 Across
19. 2 x 7 Down – 14 Down
21. 8 x 19 Across + 27 Across
24. 2 x 19 Across – 5 Across
25. 4 x 5 Across + 19 Across
26. 4 x 10 Across + 15 Across
28. 4 x 19 Across + 18 Down
29. 4 x 13 Down + 9 Down

Down

1. 8 x 5 Across + 27 Across
2. 2 x 7 Down – 24 Across
3. 3 x 26 Across + 2 x 19 Across
4. 4 x 22 Down + 12 Across
5. 4 x 19 Across + 24 Across
7. 4 x 8 Across + 27 Across
9. 4 x 24 Across + 1 Down
13. 4 x 5 Across + 24 Across
14. 4 x 8 Across + 25 Across
17. 4 x 10 Across + 5 Across
18. 12 x 27 Across + 1 Down
20. 4 x 17 Down + 22 Down
21. 4 x 8 Across + 1 Across
22. 2 x 27 Across – 8 Across
23. 4 x 2 Down + 6 Across
24. 4 x 15 Across + 19 Across

Contest Rules: All entries must be received by February 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.

Solutions to December's Puzzles:

Guest CrossNumber 1
Circular Park
Solution:

Let CF be X yards. Then AF = (4/3)X and BF = (36/15)X

Then X x 96 = (4/3)X x (36/15)X. therefor X = 30, BF = 72 and AF = 40. Lines EH and GH are the perpendicular bisectors of the chords AB and CD, making H the center.
DH2 = GH2 + GD2. Where GH = (72 + 40)/2 – 40 = 16 and GD = (96 + 30)/2 = 63.

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