Alice Meets the Infamous Mad Hatter
04/01/2001
by K.H, "Wicks" Wickremasinghe
At his tea party, the Mad Hatter said, "I have noticed something about my age. If you add the square of its second digit to twice the square of its first digit, you get the same number as my age."
"That's nothing strange," said Alice, showing a sad lack of respect for her elders. "That trick works for my mother's age and for my father's age, and for my brother's too. He's older than her, you know."
"Is your brother older than your mother?" asked the dormouse.
"Certainly not. I meant that my father is older than my mother," replied Alice indignantly.
"Then why don't you say so?" grumbled the dormouse and went back to sleep.
What were their respective ages?
Grand Prize Winners
Congratulations to Paul Morgan of K & F Electronics Inc. for solving the Boxes for Birthday Presents challenge, and to Frank Strobl of Central Steel & Wire Co. for solving CrossNumber 59.
CrossNumber 61
No number is repeated. Root means square root.
Across
 |
1. 7 Across x 13 Across
3. See 17 Across
6. 13 Across + (2 x Root of 3 Down)
7. Prime
8. Prime, 16 Down big ÷ Root of 3 Down
10. Prime
11. See 19 Across
12. 3 x 17 Across big ÷ 4
13. 10 Across - (2 x 7 Across)
15. Prime, greater than
17 Across
17. 4 x Root of 3 Across
18. (2 x 6 Across) + 16 Down
19. 8 Across x Root of 11 Across
Down
2. 8 Across x Root of 9 Down
3. See 17 Down
4. (12 Across x 13 Across) big ÷ 6
5. (10 Across x 12 Across) big ÷ 6
9. See 2 Down
12. Root of (9 Down x 11 Across)
14. 4 x 15 Across
16. (10 x 10 Across) - 7 Across
17. (2 x 3 Down) - (12 Across big ÷ 2)
Contest Rules: All entries must be received by May 1, 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 February's Puzzles
CrossNumber 59
 |
An alternate correct answer for 10 Across is 61, which affects the answers to 18 Across, 17 Down, 16 Across, 16 Down and 15 Down. Both sets of correct answers were deemed winners and placed in the drawing.
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The Boxes for Birthday Presents
Answer: 21 inches by 20 inches
Solution: Because the volume and weight are equal, it is necessary to consider the dimensions of the sides only. 37, the length of the diagonal, can be put as the sum of two squares only as 62 + 12 = 37. Then, by the well-known formula for Pythagorean triangles, a = 2 mn, b = m2 - n2, c = m2 + n2, b = 35 and a = 12. The area is 420 square inches. The only other factorial of 420 to give a Pythagorean triangle is 21 x 20 inches, with a diagonal of 29 inches.