by K.H. “WICKS” Wickremasinghe
Last week a new family moved into our neighborhood. My daughter soon made friends with a girl, Susan, in that family.
I should have known better, but I asked my daughter, “How old is your new friend?”
“The ages of all the females in the family total 59 years and the males 65 years. If they live here another two years, the father will be six times as old as Susan will be,” said my daughter. (I didn't want to tell here that it would be the same if they didn't stay here another two years.)
“Two years ago when they lived in Los Angeles, the mother was four times as old as the twins, Jack and Jill, were. When the twins are twice as old as they are now, David will be eight years older than Susan,” explained my daughter, with a “caught-you-Dad” look on her face.
How old are the six members of our new neighbors?
Grand Prize Winners
Congratulations to Peter Douglas of Custom Chip Connections Inc. (Huntsville, Ala.) for solving the Alice Meets the Infamous Mad Hatter puzzle, and to Gail A. Schooley of The Engineering Consortium Inc. (Santa Clara, Calif.) for solving CrossNumber 61.
CrossNumber 63
Across
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1. 5 Across + 19 Down
2. 18 Down – 21 Down
5. See 6 Down
7. 25 Across x 26 Across
9. 5 Across x 22 Down
11. See 4 Down
13. 15 Across + 2
14. See 20 Across
15. (2 Across x 27 Across) ÷ 4
16. (1 Across x 27 Across) ÷ 2
18. 8 Down x 21 Down
20. 18 Across – (2 x 14 Across) ÷ 3
23. 10 Down – 10 x 14 Across
25. (5 Across + 3 Down) ÷ 2
26. 18 Down + 21 Down
27. See 15 Across
Down
1. 5 Across x 21 Down
2. 3 x (14 Across + 21 Down)
3. See 25 Across
4. 11 Across + 20 Across
6. 5 Across squared
7. See 18 Down
8. See 18 Across
10. 1 Across x 6 Down
12. 5 Across x 6 Down
16. 17 Down – 9 x 1 Across
17. 1 Across squared
18. 7 Down squared
19. 5 Across x 5 ÷ 2
21. See 24 Down
22. 27 Across squared
24. Square root of (21 Down x 22 Down)
Contest Rules: All entries must be received by June 25, 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 May's Puzzles
CrossNumber 61
Alice Meets the Infamous Mad Hatter
Answer: Mad Hatter 34, Brother 24, Father 51, Mother 50
Solution: Let the age be 10x + y, then y2 + 2x2 = 10x + y
ie: y2 – y + 2x2 – 10x = 0
(1) 2y = 1 ± √ (1 – 8x2 + 40x)
Let 1 – 8x2 + 40x = k2
ie: x2 – 5x + (k2 – 1) ÷ 8 = 0
(2) 2x = 5 ± √ [25 – (k2 -1) ÷ 2]
Let [50 – (k2 – 1)] ÷ 2 = z2
ie: 2z2 + k2 = 51
ie: z = 1 and k = 7 or z = 5 and k = 1
If k = 7, substituting in equation (2), 2x = 5 ± 1, x = 2 or 3
Substituting in equation (1), 2y = 1 ± 7, so y = 4, therefor the ages are 24 and 34.
Similarly if k = 1, substituting in equation (2), 2x = 5 ± 5, x = 5.
Substituting in equation (1), 2y = 1 ± 1, y = 1 or 0. Gives the value of 50 for mother and 51 for father.