Family Allowance
11/01/2000
Donald balanced his family budget with difficulty. He called his three sons - Al, the eldest, Ben and Cory, the youngest (who was four years Al's junior).
"I'm sorry to tell you, boys, that because of financial constraints, I will not be able, for the next two years, to continue (as I have been doing) giving you an allowance to be divided equally among you - equal to the product of your ages in years. I'll have to calculate the allowance assuming that Cory will not grow older. I hope you boys will understand."
Ben, who was the math whiz, did a quick mental calculation. "We'll be getting $831 less in the two years than we would have gotten. That's quite a bit of money!"
"All the same, we understand, Dad," they all chirped in unison.
What are their ages now?
Grand Prize Winners
Congratulations to our most recent winners: Sandy Hajec at Delphi Delco Electronics Systems, for solving the Real Estate puzzle, and Robert Feiss at Shure Inc., for solving CrossNumber 55.
CrossNumber 57
In this CrossNumber, some of the clues are blank; the puzzle can be solved without clues for these numbers. All two-digit numbers are prime. No number is repeated.
Across
 |
1.
2. 14 Across squared
4.
6.
7.
9. 3 x 6 Across
12. See 26 Across
14.
15. 14 Across x 17 Across
17.
18. 17 Across squared
22. 4 Across x 27 Down
25. 2 Across + 12 Across + 1 8 Across
26. 3 x 12 Across
27. 17 Across x 29 Down
28. See 15 Down
30. 29 Down squared
31. 27 Down squared
Down
1. 4 Across squared
2.
3.
5. 1 Across squared
6.
8.
10.
11. 10 Down + 27 Across
13.
15. 4 x 28 Across
16. 1 Down - (2 x 2 Across)
20. (4 x 17 Across) squared
21. 14 Across + 30 Across
23. 10 x 26 Across
24. 4 x (8 Down squared)
27.
29.
Solutions to September's Puzzles:
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 CrossNumber 55 |
Real Estate
Answer: 240,240; 124,320; 104,040 and 201,720 square feet for A, B, C and D.
Solution: Let m, n be the dimensions of an allotment.
m2 + n2 = 6972 = (41 x 17) x (41 x 17) = 412 x 172 = 289 x 1681
But (1): 697 = 112 + 242 (a) or 162 + 212 (b)
(2): 289 = 82 + 152 = 172 (c)
(3): 1681 = 402 + 92 = 412 (d)
Using (a2 + b2)2 = (a2 - b2)2 + (2ab)2
From (a), (697)2 = (112 + 242)2 = (242 - 112)2 + (2 x 11 x 24)2 \ : = 242 - 112 = 35 x 13 = 455 n = 2 x 11 x 24 = 528, Area 240,240 sq. ft.
Similarly from (b), m = 672 and n = 185, Area 124,320 sq. ft.
From (c) and (d), m2 + n2 = {41 √(82 + 152)}2 = 412 x 82 + 412 x 152\m = 41 x 15 and n = 41 x 8 giving m = 615 and n = 328, Area 201,720 sq. ft.
Similarly from (d) and (c), m2 + n2 = {17 √(402 + 92)}2 = 172 x 402 + 172 x 92
Giving m = 680 and n = 153, Area 104,040 sq. ft.
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Contest Rules: All entries must be received by Dec. 29, 2000. 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 in order to be considered. Employees of PennWell and their immediate families, agents contracted by PennWell and their immediate families, employees of PennWell and its subsidiary companies and their immediate families, and members of the Advanced Packaging Advisory Board and their immediate families, are not eligible to compete.