Think Tank

by K.H. “Wicks” Wickremasinghe

The Natural Lawnmower
Farmer Giles had an equilateral-triangle-shaped lawn with a side of 42 yards. Being too lazy to mow such a large area, he bought a goat to eat the grass. Being a parsimonious chap, he bought a rope only 21 yards long. The first day he tied the goat to one apex of the triangle so that the goat could eat a sector of 21 yards (radius). The next day he tied the goat to another apex and the third day to the third apex. Then he used his weed eater to mow the uneaten part of the lawn.

What is the area of the lawn that the farmer had to mow? Assume that square root of 3 is 1.73 and pi is 22/7.

New Winners
Congratulations to Adam Schubring of Visteon Corp. (Dearborn, Mich.) for solving the Way to the Slumber Party Challenge, and to Dennis J. Tebaldi of Goodrich Corp. (West Hardford. Conn.) for solving CrossNumber 69!

CrossNumber 71

Across
1. 17 Across + 18 Across + 2 x 4 Down
4. 9 Across + 22 Across + 28 Down
6. 22 Down squared – 3 x 18 Across
9. 12 Across – 28 Down Prime
11. 16 Down + 3 x 30 Across
12. 17 Across – 15 Across
13. 28 Down + 30 Across Prime
15. 20 Down / 2 – 4 Down
17. 2 x 4 Down + 10 x 22 Across
18. 17 Across + 27 Down – 2 Down
19. 12 Across + 23 Across + 27 Down
21. 4 Down + 18 Across – 1
22. 4 Across – 12 Across
23. 4 Across + 17 Across + 18 Across
25. 27 Down / 2 Prime
27. 17 Across squared – 18 Across – 14 Down
29. 2 x (18 Across + 1)
30. 25 Across + 4 x 9 Across

Down
1. 22 Down + 2 x 30 Across
2. 3 x 22 Across
3. 3 x (2 Down + 4 Down + 15 Across)
4. 16 Down – 22 Down
5. 15 Across + 21 Across – 30 Across
7. 22 Across x (4 Across + 9 Across) / 8
8. 2 x 21 Down
10. (11 Across + 2 x 22 Across) x (28 Down – 4 Down)
12. (19 Across – 17 Across) x (16 Down + 28 Down) /2
14. 22 Across + 26 Down – 28 Down
16. 4 Down x 28 Down / 4
20. 16 Down + 22 Across + 22 Down
21. 2 x (2 Down + 27 Down)
22. 22 Across + 2 x 27 Down
24. 29 Across + 12 Across / 5 Prime
26. 3 x (22 Down + 25 Across)
27. 2 Down + 22 Across – 4 Down
28. 9 Across + 4 Down / 2

Contest Rules: All entries must be received by March 29, 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.

Solutions to January's Puzzles:

CrossNumber 69

Way to the Slumber Party

Solution: Let number be ABCD. Then Dotty's number is 5 + 2(ABCD). Because 2(ABCD) + 5 = DCBA, which is a 4 digit number, A is less than 5.

Also 2D + 5 = A or A + 10. Thus, A is odd and can only be 1 or 3. Hence, D can be only 3 or 4.

Since 2 x A or 2 x A + carry over of 1 = D, D can only be 3 and A = 1.

Now (1BC3) x 2 + 5 = 3CB1. 2 x 3 + 5 produces a carry over of 1. 2C + the carry over of 1 gives B. Therefore, B is odd. Also (BC x 2) + 1 must have a carry over of 1 to give D = 3. Thus, BC > 49. Therefore, B = 5, C = 2 or 7 or B = 7, C = 3 or 8, or B = 9, C = 4 or 9.

B = 5, (1523) x 2 + 5 = 3051 or (1573) x 2 + 5 = 3151. Neither of which is the original number reversed.

B = 7 and C = 3 (or 8) does not satisfy the required conditions. B = 9 and C = 4 does not give a valid answer. But B = 9 and C = 3 gives (1993) x 2 + 5 = 3991.