The total for Alice, Bob and Carol, 49, is 11 higher than that the total of 38 for Harry, Alice and Bob, so Carol's score thus far was 11 higher than Harry's. Going around the circle, we find similarly, using their initials as their totals:
D - A = -4
E - B = 3
F - C = 4
G - D = -8
H - E = -5
A - F = 9
B - G = -10
Relative to Harry, then, the other scores are:
A = H + 24
B = H + 2
C = H + 11
D = H + 20
E = H + 5
F = H + 15
G = H + 12
The first of the above was of course C = H + 11, already mentioned; then, as F = C + 4, it follows that F = H + 15; etc.
The total of all the numbers given, 38, 49, 45, 48, 52, 44, 39 and 48, was 363, which was three times the total of the people's scores, which was therefore 121. But, counting Harry, the total of the scores is 8*H + 89, so Harry's score, H, is 4, and the other scores can be obtained from the table above:
H = 4
A = 28
B = 6
C = 15
D = 24
E = 9
F = 19
G = 16
Based on Enigma No. 1620, "Pieces of eight", by Gwyn Owen, New Scientist, 6 November 2010, page 28. |