by K.H. “Wicks” Wickremasinghe
“I know that you wanted only 10, 100, 10K and 100K Ohm resistors for your school project (SP), but I bought a box that contains more than the quantities you need, as well as several resistors of other values,” said Tom's dad.
“I'll use what I need for my SP, and the spare 10½ and 10K½, as well as half of the spare 100½ and 100K½, for my model train set (MT). Dad, you can use all the rest for the burglar alarm system (BA) you want to build,” answered Tom.
They ended up using the same number – each one quarter of the total for their MT and BA. One half of Dad's share was made up of the other values, and he used the same number of 100s and 100Ks. Tom used one more 10K than 100K, and his10Ks and 100Ks combined equaled the number of 100s he needed for his SP. The total number of 100Ks equaled the number of 100s and 10Ks combined that Tom needed for his SP. The total of 100Ks and 10Ks Tom needed for his SP was three times the number of 100s Dad used, and the total of 10s and 100s Dad bought was five times the number of 100Ks Tom needed for his SP.
How many of each did Tom use for his SP, and what was the total number of resistors in the box?
CrossNumber 52 (All answers are numbers. No number is repeated, none begins with zero and “root” means “square root.”.)
Across
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1. See 20 Down
5. Square
8. Square
9. Square
10. Root of 16 Across x (12 Down + 13 Across)
12. Root of (20 Across x 24 Down)
13. Root of (1 Down x 24 Down)
14. 4 Down x Root of 30 Down
16. See 31 Across
18. See 26 Down
20. See 21 Down
22. See 27 Across
23. Root of (3 Down x 30 Down)
25. Root of (1 Down x 3 Down)
27. 22 Across x Root of 22 Across
29. Square
31. 16 Across x Root of 16 Across
32. Root of (3 Down x 16 Across)
Down
1. See 13 Across
2. 1 Down x 11 Down x 27 Down
3. Square
4. Root of (7 Down x 24 Down)
5. Square
6. 12 Down x (5 Down + 12 Across)
7. See 4 Down
11. Root of 24 Down
12. Root of 17 Down
13. Square
15. 20 Down x 22 Across
17. See 12 Down
19. 4 Down x 16 Across
20.Root of 1 Across
21. Root of 20 Across
22. 5 x 31 Across – 2 x 30 Down
24. See 11 Down
26. 18 Across x Root of 18 Across
27. Root of 31 Across
28. Root of (9 Across x 22 Across)
30. See 23 Across
Contest Rules: All entries must be received by July 20, 2000. The winners of the word puzzle and CrossNumber (can be the same person) will be drawn from all correct entries. Fax entries to 847-634-4240. All entries must include name, complete address, company affiliation and daytime phone number 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.
Grand Prize Winners
As always, a host of enthusiastic and competitive readers responded to our April puzzles. Congratulations to: Peter Douglas of Custom Chip Connections for the Birthday Party challenge, and Ronald Keukelaar of Dytak Corp. for CrossNumber 51. They are the lucky recipients of our exclusive Advanced Packaging T-shirts, and we hope they'll wear them with pride. Good luck to all of you as you attempt to solve this issue's puzzles. Don't forget to fax in your solutions – you could be our next winner!
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Solutions to April's Think Tank Puzzlesellipse
Birthday Party
Answer: Each boy receives 208 marbles
Solution: Let the number of boys be x, and the number of girls be (x-5).
Let the number of marbles per boy be y, and those per girl be (y – 7).
xy + (x-5)(y-7) = 2,267
2xy – 7x – 5y + 35 = 2, 267
\4xy – 14x – 10y + 35 = 4,534 – 35 = 4,499
\(2x-5)(2y – 7) = 11 x 409 [both prime numbers]
\2x – 5 = 11, which gives x = 8 and 2y – 7 = 409, which gives y = 208
Each boy receives 208 marbles.