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?

this program first creates a list of all primes less than 45, then it goes through all possible choices of 3 different primes from that list.  These 3 represent the 3 primes not used for the players.  Then to get the players average I simply subtracted their sum from the total sum.  I then tested if the average was prime and printed the 3 primes and the average if it was.  Of the 3 results only the first gives a prime average that is not a team number.

thus the team numbers are

5,7,11,13,17,19,29,31,37,41,43 with average 23

Pr={};

For[i=2,i<45,i++,

If[PrimeQ[i],

Pr=Append[Pr,i]];

];

lng=Length[Pr];

tot=Total[Pr];

For[i1=1,i1£12,i1++,

For[i2=i1+1,i2£13,i2++,

For[i3=i2+1,i3£14,i3++,

p1=Pr[[i1]];

p2=Pr[[i2]];

p3=Pr[[i3]];

v=p1+p2+p3;

avg=(tot-v)/11;

If[PrimeQ[avg],

Print[p1,",",p2,",",p3,",",avg];

];

];

];

];

this returns

2,3,23,23

2,7,19,23

2,29,41,19

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Posted by Daniel on 2009-02-19 11:55:21