Long ago, there was a king who had six sons. The king possessed a huge amount of gold, which he hid carefully in a building consisting of a number of rooms. In each room there were a number of chests; this number of chests was equal to the number of rooms in the building. Each chest contained a number of golden coins that equaled the number of chests per room. When the king died, one chest was given to the royal barber. The remainder of the coins had to be divided fairly between his six sons.

Now: Is a fair division possible in all situations?

Yes. x^3-x = 0 mod 6.
1-1 = 0
8-2 = 6 = 0
3*3*3-3 = 8*3 = 2*3 = 6 = 0
4*4*4-4 =15*4=3*4=12=0
5*5*5-5 = 24*5 = 0*5 = 0
0^3-0=0

      

Posted by Michael Boger on 2005-10-12 18:13:58