# 1997 MIT Mystery Hunt Puzzle 16 Solution

A rood is an old English unit equal to 1/4 acre or 10890 square feet. In 1939, in the pre-decimalization English currency, a shilling was 1/20 pound.

38720 5
4 91 44
0 2 384
1110
72 1918
9   792
27 16 9

The outlined regions contain the numbers 20, 14, 21, 18, and 7, which correspond to the letters TNURG, which rearranges to the answer GRUNT.

Detailed solution

15 across is a 2-digit cube, hence 27 or 64. The walking speed is 3 or 4 mph, which (in units more useful for the rest of the puzzle) is either 88 or 117 1/3 yards per minute.

11 across is a year starting with a 1. Since this 1 is the last digit of 9 down, and by its clue, 9 down times 10 across gives 10 down, 10 down and 10 across must end with the same digit. Since 10 down and 10 across also start with the same digit, 10 down must be less than 20 times 10 across, so 9 down is 11.

8 across is also a year starting with a 1. Then 8 down starts with 1 and ends with the same digit which is the first digit of 15 across. So if he walks 88 yards/minute, he takes 12 minutes to walk 4/3 the perimeter, or 1056 yards, so the perimeter is 792 yards. If he walks 117 1/3 yards/minute, he takes 16 minutes to walk 4/3 the perimeter, or 1877 1/3 yards, which makes the perimeter 1408 yards. But by 14 across, the perimeter is a three-digit number of yards, so the former case must be correct: 15 across is 27, 8 down is 12, and 14 across is 792.

From its clue, 16 across is 27 - 11 = 16.

12 down is 1 + the sum of the digits of 10 down, and it ends with a 9, so it can only be 19. This makes 10 down 792, and 10 across, Lord Presley's age, is 72.

11 across is the year Lisa, Lord Presley's daughter, was born. 181X here would make her at least 120 years old in 1939, too old, so it must be 191X and Lisa is in her 20s.

7 down is the square of the width of the lot, and it is five digits ending with 976. This can only be 30976, and the width is 176 yards. This makes the length of the lot 220 yards, so 6 across is 220 - 176 = 44.

The area is 220 * 176 = 38720 sq. yards and this is 1 across). A rood is 10890 sq. ft. or 1210 sq. yards, so the area is 32 roods. So 7 across is 32*12 = 384.

6 down is now 48. This is Michael's age in 1939, and in 1945 he is 54, twice Lisa's age then, so Lisa is 27 then and 21 in 1939. So the year of Lisa's birth for 11 across is 1918.

Now 13 down indicates Graceland-on-Avon has been in the Presley family for between 820 and 829 years. That means the year of acquisition in 8 across is 1110, and 13 down is 829.

2 down is now a square 7XX1, which can only be 7921, the square of 89.

The value of the land is 4 down = 1 down * 7 across / 240 = 1 down * 8/5. Since 1 down starts with 3 and 4 down ends with 44, the only combination that works is 1 down 340, 4 down 544.