All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Contestants in a Circle (Posted on 2011-01-31) Difficulty: 2 of 5
The eight contestants were seated at a circular table in alphabetic order clockwise: Alice, Bob, Carol, Dave, Eve, Frank, Gisele and Harry. Some points had already been awarded by the judges, in varying amounts to the different competitors, but the competitors didn't know what their totals were. As a last competition, they were to deduce all their scores thus far based upon the announcement of eight totals of three contestants' scores, each total being the sum of three successive people around the table, so for example, the total for Harry, Alice and Bob (the triplet centered on Alice) was given as 38.

The successive triplets centered on Bob through Harry totaled as follows: 49, 45, 48, 52, 44, 39 and 48.

What were in fact the individual scores to that point in the competition?

  Submitted by Charlie    
No Rating
Solution: (Hide)
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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: easy way outbroll2011-02-01 02:39:30
Solutioneasy way outAdy TZIDON2011-01-31 18:21:11
Possible solutionbroll2011-01-31 15:20:03
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information