# Think Tank

by K.H. “Wicks” Wickremasinghe

1,001 Nights
For 1,001 nights, the princess related stories to the sultan. At the end of this time, the sultan said, “Do you know the number of nights that we had musicians entertaining us at dinner?”
The princess responded, “How would I remember that? I have told stories for more than two years.”
“The square of the number of nights we had musicians is the product of the number of nights we had jugglers entertainning. We had entertainers every night,” he said.
“That's still not fair – that problem has three possible solutions,” she said.
“If I tell you that the number is less than 100, would you be able to solve it?” he asked her.
Of course she did. Can you?

Grand Prize Winners
Congratulations to Anthony Vigliotti of American Competitiveness Institute (Philadelphia, Pa.) for solving the Natural Lawnmower Challenge, and to Dinah Teng of Engage Electronics Pte. Ltd. (Singapore) for solving CrossNumber 71!

CrossNumber 73
In this grid, no number is repeated or begins with zero. The two-digit answers are prime, squares or cubes. Apart from the squares of these 10 numbers, all the three-digit answers are prime. With the few clues given below, you should be able to complete the CrossNumber.

Across
4. 28 Down squared
30. 4 Down squared

Down
2. 1 Down squared
5. 16 Across squared
7. 6 Down squared
8. 4 x 15 Across + (3 x 9 Down)
14. 26 Down squared
15. 9 Down squared
18. 25 Down squared
19. 9 Down + (4 x 16 Across)
20. 17 Across squared
22. 24 Down squared

Solutions to March's Puzzles:

CrossNumber 71
The Natural Lawnmower

Solution: The area of an equilateral triangle with side 42 is 21 x 21 √ 3 = 762.93 square yards.

Each day the goat eats a sector of a circle with a radius of 21 yards and an angle of 60°, which would be 1/6 of the area of the circle with a radius of 21 yards. Therefore, 22/7 x (21 x 21) / 6 = 231 square yards. The area of three such areas is 693; the remaining area to be mowed is 762.93 – 693 = 69.93.

Contest Rules: All entries must be received by May 31, 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.

online
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