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The Prime Time Soccer Team (Posted on 2009-02-19) Difficulty: 3 of 5
Each of the 11 players on the Prime Time soccer team was identified by a different prime number less than 45 on his jersey. The average of those primes was also a prime different from each of those of the players. What were the players' identifying numbers?

  Submitted by Charlie    
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Solution: (Hide)
   10   for A=1 to 4
   20   for B=A+1 to 5
   30   for C=B+1 to 6
   40   for D=C+1 to 7
   50   for E=D+1 to 8
   60   for F=E+1 to 9
   70   for G=F+1 to 10
   80   for H=G+1 to 11
   90   for I=H+1 to 12
  100   for J=I+1 to 13
  110   for K=J+1 to 14
  200     Tot=prm(A)+prm(B)+prm(C)+prm(D)+prm(E)+prm(F)+prm(G)+prm(H)+prm(I)+prm(J)+prm(K)
  210     Avg=Tot//11
  220     if Avg=int(Avg) then
  230       :if prmdiv(Avg)=Avg then
  240         :print prm(A);prm(B);prm(C);prm(D);prm(E);prm(F);prm(G);prm(H);prm(I);prm(J);prm(K),Avg
  999   next:next:next:next:next:next:next:next:next:next:next

finds

3  5  7  11  13  17  19  23  31  37  43         19
3  5  11  13  17  23  29  31  37  41  43        23
5  7  11  13  17  19  29  31  37  41  43        23

The average is shown as the last number on the line. In the first two instances, the average repeats one of the players' numbers, so the last line contains the players' numbers and the average, 23.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionTwo when not reading the question, but then....brianjn2009-02-19 18:19:47
Some ThoughtsInitial ThoughtsAndre2009-02-19 12:12:13
Mathematica SolutionDaniel2009-02-19 11:55:21
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