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?

Arnold---61--67--71--79 = 278

Brian----62--65--74--77 = 278

Chuck---63--68--72--75 = 278

Denis----64--66--70--78 = 278

First test Arnold (4 of 5 primes) and Brian (4 of 5 semiprimes). Since they must have the same four-rounds score, the only sum is 278.  Then assign four of the ten remaining scores (60..79) to Chuck and Denis so each totals 278, and apply "v" test.  QED

 

Posted by ed bottemiller on 2009-11-30 13:26:02