Nowhere City
09/01/2001
BY K.H. "WICKS" WICKREMASINGHE
I did not fancy the idea of going to "Nowhere City," a place that was not even marked on the map, on a road that had no name. However, as I was driving along, I noticed the mile posts alongside the road. "At least I'll know how far away Nowhere City is when I get there," I thought. No such luck! Suddenly, the mile posts vanished. After a few more miles, they reappeared but it was too dark to see any markings on them.
When I finally reached "Nowhere City," I walked into the first pub I saw. I mentioned the missing mile posts to the bartender and he said, "An even number of mile posts at the center are missing, and the sum of the numbers on the missing posts is 2,563."
How many mile posts were missing, and what is the distance to Nowhere City?
Grand Prize Winners
Congratulations to Thang Tak Seng of Infineon Technologies AP Pte. Ltd. (Singapore) for solving Seniors' Ages, and to Brent Lybrand of Specialty Electronics (Landrum, S.C.) for solving CrossNumber 64.
CrossNumber 66
Each number appears only once. No number begins with zero.
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Across
1. 13 Across x 15 Across ÷ 2
3. 7 Across + 8 Down
5. 17 Across + 18 Across
7. 15 Down - 13 Across
10. Prime
11. Prime
12. 30 Across squared
13. 1 Across + 15 Across - 5 Across
15. 1 Across - 18 Across - 32 Across
17. Prime
18. Prime
22. 10 Across + 17 Down
25. 12 Across - 23 Down
27. 7 Across + 24 Down - 15 Across
28. 13 Across x 32 Across
30. 3 Across + 32 Across - 10 Down
31. 10 Across + 11 Across
32. 18 Across - 13 Across
Down
1. 1 Across squared
2. 4 x 7 Across
4. 10 Across + 10 Down
5. 32 Across squared
6. 5 Across squared
8. Prime
10. Prime
14. 15 Across squared
15. 13 Across squared
16. 13 Across + 2 x 27 Across
17. 7 Across + 10 Across
20. Square root of (17 Across x 17 Down)
21. 16 Down + 32 Across - 31 Across
23. 26 Down + 5 Across ÷ 2
24. 30 Across x 32 Across
26. 15 Down + 30 Across - 32 Across
Contest Rules: All entries must be received by September 28, 2001. 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.
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Solutions to July's Puzzles
CrossNumber 64
Seniors' Ages
Answer: Al = 64, Ben = 86, Cam = 85, David = 88, Ezra = 73, Fred = 96.
Solution: Let the six ages be a, b, c, d, e and f, denoted by the first letter of the person's name. Average age of all six:
A = (a + b + c + d +e + f) ÷ 6
therefor 6A = (a + b + c + d + e + f)
Also, f = 3a ÷ 2 (i)
3.6 = (b + c + d + e + f) ÷ 5 - A
From (1): 3.6 = (b + c + d + e + f) ÷ 5 + (a ÷ 5) - (a ÷ 5) - A
= 6A ÷ 5 - (a ÷ 5) - A
= (A - a) ÷ 5
therefor 18.0 = A - a (6)
Similarly from (2), (3), (4) and (5):
9.0 = A - e
Giving:
A - a = 18.0
A - e = 9.0
A - c = -3.0
A - b = -4.0
A - d = -6.0
Adding 5A - (a + b + c + d + e) = 14
5A - (6A - f) = 14
therefor f = 14 + A (11)
From (i) and (II):
therefor a = 82 - 18 = 64, b = 86, c = 85, d = 88, e = 73, f = 96