# Think Tank

by K.H. “Wicks” Wickremasinghe

Couples Cruise
The “Couples Only” Cruise had 1,100 married couples as passengers. Four-fifths of the husbands who were taller than their wives were also older. Five-sixths of the husbands who were older than their wives were also taller.
There were 143 wives who were taller and older than their husbands.
How many husbands were taller and older than their wives?

Grand Prize Winners
Congratulations to David Turner of Bourns Inc. (Logan, Utah) for solving the Nowhere City chal-lenge. There were no winners for CrossNumber 66 – perhaps one of our trickiest challenges yet. Good luck this month!

CrossNumber 68

## Across

1. (3 x 7 Across)2 x 2 – 2000
5. (7 Across)2 + 3 Down + 1
6. (8 Down + 1) ÷ 3
7. (6 Across ÷ 4)3
8. 28 x 6 Across + 3√(8 Across)
9. (3 Down)4

## Down

1. (7 Across – 1)3 – [3 Down + √(3 Down)]2
2. √4 Down – 4√(3 Down)
3. (6 Across ÷ 6)4
4. (6 Across)4
7. 20 x 6 Across + 3
8. 5 x 3√(8 Across)

Contest Rules: All entries must be received by December 3, 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.

Solutions to August's Puzzles

CrossNumber 66

This tricky puzzle is in base 9. Note that the grid did not have 9, 19 or 29.

Nowhere City
Answer: 22 posts were missing, and the distance was 232 miles.*
Solution: Let 2n be the number of missing posts and the number on the two missing center posts be (a) and (a + 1).

a – (n – 1)…(a – 2), (a – 1), a, (a + 1 ), (a + 2)…
(a + n)

Adding the first missing to the last missing, second missing to one but last missing, etc., we get the value 2a + 1.

Then n(2a + 1) = 2,563 = 11 x 233

Giving 2n = 22 and 2a = 232.

*Alternate answer: 2 missing posts, with a distance of 2,562 miles. Perhaps Wicks will be more merciful this month . .