Answers to Mind Games on the Web

Vol 3, No 2 Answers Presented by the Smart Science ® system and Bill Graham as a free service for entertainment and education
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ANSWERS TO
A MOST UNUSUAL PUZZLE

by Bill Graham

Dog's Mead Puzzle The hint from last time was to find a good place to start. I started in the bottom half. The complete solution is below.

8 ACROSS and 11 ACROSS are four-digit years; both should start with a 1. Note that 9 DOWN ends in a 1.
15 ACROSS ("Cube of Farmer Dunk's walking speed") can only be 27 (3³) or 64 (4³). However, if 15 ACROSS is 64, then 16 ACROSS ("15 ACROSS minus 9 DOWN") would end in a 3, and 7 DOWN ("Square of the breadth of Dog’s Mead") would also end in a 3, which is impossible. (No square ends in 3.) So, 15 ACROSS is 27.
16 ACROSS equals "15 ACROSS minus 9 DOWN". But the first digit of 9 DOWN can only be 1. Leading zeroes are not allowed (for either 9 DOWN or 16 ACROSS). Thus, 16 ACROSS must be 16 and 9 DOWN must be 11.
Since 9 DOWN equals "The number, which multiplied by 10 ACROSS, gives 10 DOWN", 10 ACROSS must end with a 2.

8 DOWN ("Time in minutes it takes Father Dunk to walk 1 1/3 times around Dog’s Mead") is therefore 12; the number of minutes in which farmer Dunk walks 1 time around Dog's Mead is 9; and (from 15 ACROSS) it follows that farmer Dunk walks 3 miles per hour. 14 ACROSS ("Perimeter in yards of Dog’s Mead ") is 792.
12 DOWN ("Sum of the digits of 10 DOWN plus 1") can now only be 19.
11 ACROSS ("Year of Mary’s birth") must start with 191, and since the current year is 1939, 3 DOWN ("Age of Mary, Father Dunk’s daughter") must start with a 2.
Since 6 ACROSS ("Difference in yards between length and breadth of Dog’s Mead") is at least 10 and at most 99, and the sum of the length and width of Dog's Mead equals 396 (because of 14 ACROSS), the minimum value for the width is 149 and the maximum value is 193. Because of 7 DOWN ("Square of the breadth of Dog’s Mead"), the width must end on a 4 or a 6. Therefore, only eight possible values remain: 154, 156, 164, 166, 174, 176, 184, and 186. Of these values, only 176 has a square that ends on 976. Now we can calculate that the length of Dog's Mead is 220, that 7 DOWN ("Square of the breadth of Dog’s Mead") is 30976, that 1 ACROSS ("Area in square yards of Dog’s Mead") is 38720, that 6 ACROSS ("Difference in yards between length and breadth of Dog’s Mead") is 44, and that 7 ACROSS ("Number of roods in Dog’s Mead times 8 DOWN") is 384.

Since 6 DOWN ("Age of Ted, Father Dunk’s son, who will be twice the age of his sister Mary in 1945") is 48, we can calculate that 3 DOWN ("Age of Mary, Father Dunk’s daughter") is 21 and that 11 ACROSS ("Year of Mary’s birth") is 1918.
13 DOWN ("Number of years Dog’s Mead has been in the Dunk family") can now only be 829, and therefore 8 ACROSS ("The year the Dunks acquired Dog’s Mead") is 1110.
Because of 9 DOWN ("The number, which multiplied by 10 ACROSS, gives 10 DOWN") and 12 DOWN ("Sum of the digits of 10 DOWN plus 1"), 10 ACROSS ("Father Dunk’s age") can only be 72 and 10 DOWN ("See 9 DOWN") can only be 792.
Since 2 DOWN ("Square of the age of Father Dunk’s mother-in-law") is a number of four digits, starting with a 7 and ending on a 1, the age of the mother-in-law of Farmer Dunk is at least 84 and at most 89. Of these numbers, only 89 has a square that ends on a 1. Therefore, 2 DOWN is 7921.
From the description of 1 DOWN ("Value in shillings per rood of Dog’s Mead") we can deduce that the price per rood is at least 15 and at most 19 pounds. Since the area of Dog's Mead is 32 roods (see 1 ACROSS), and because of 4 DOWN ("Value in pounds of Dog’s Mead"), the price per rood can only be 17 pounds, and we find that 1 DOWN is 340 and 4 DOWN is 544.

I sincerely hope you enjoyed this.

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