 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Tricky Tournament Treat (Posted on 2009-11-30) Four friends, Arnold, Brian, Chuck and Denis, just played four rounds of a golf tournament. Their scores were all tied, even though the individual scores for the 16 rounds were all different. It is further known that:

(i) The 16 scores were all in the 60s and 70s.

(ii) All four of Arnold's scores were a prime.

(iii) All four of Brian's scores were semiprimes.

(iv) None of Chuck's or Denis' scores was either prime or semiprime.

(v) Chuck's lowest round was better (lower) than Denis� lowest round. Chuck's worst round was better than Denis� worst round.

What was the score of each of the golfers for the four rounds?

 See The Solution Submitted by K Sengupta No Rating Comments: ( Back to comment list | You must be logged in to post comments.) Solution Comment 3 of 3 | Arnold: 61 + 67 + 71 + 79 = 278
Brian : 62 + 65 + 74 + 77 = 278
Chuck : 63 + 68 + 72 + 75 = 278
Denis : 64 + 66 + 70 + 78 = 278

The score of each of the golfers for the four rounds was 278.

The four round score can be deduced from the first three clues....(i), (ii) and (iii):
Four distinct primes between 60 and 79
{61, 67, 71, 73, 79}:
61 + 67 + 71 + 73 = 272
61 + 67 + 71 + 79 = 278 <---
61 + 67 + 73 + 79 = 280
61 + 71 + 73 + 79 = 284
67 + 71 + 73 + 79 = 290
Four distinct semiprimes betwen 60 and 79
{62, 65, 69, 74, 77}:

62 + 65 + 69 + 74 = 270
62 + 65 + 69 + 77 = 273
62 + 65 + 74 + 77 = 278 <---
62 + 69 + 74 + 77 = 282
65 + 69 + 74 + 77 = 285
The only common value between each of the sums of  four primes and four semiprimes is 278.

There are eight sets of non-prime, non-semiprime numbers inclusively between 60 and 79 that totals 278:
60 + 64 + 76 + 78
60 + 68 + 72 + 78
60 + 70 + 72 + 76
63 + 64 + 75 + 76
63 + 68 + 72 + 75
64 + 66 + 70 + 78
64 + 66 + 72 + 76
64 + 68 + 70 + 76
Of these, there are only three pairs of sets where the numbers are distinct:
60 + 64 + 76 + 78 <=> 63 + 68 + 72 + 75
60 + 68 + 72 + 78 <=> 63 + 64 + 75 + 76
63 + 68 + 72 + 75 <=> 64 + 66 + 70 + 78
Of these, only one pair of sets has the low and high values lower than the other:
63 + 68 + 72 + 75 <=> 64 + 66 + 70 + 78

Edited on November 30, 2009, 6:37 pm
 Posted by Dej Mar on 2009-11-30 18:00:09 Please log in:
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