Wednesday, September 3, 2008
Divide it if u can...
The legendary king Midas possessed a huge amount of gold. He hid this treasure carefully: in a building consisting of a number of rooms. In each room there were a number of boxes; this number was equal to the number of rooms in the building. Each box contained a number of golden coins that equaled the number of boxes per room. When the king died, one box was given to the royal barber. The remainder of the coins had to be divided fairly between his six sons. Is a fair division possible in all situations?
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3 comments:
k=(n^3-n)/6 by mathematical induction...
the statement results that the remaining gold will be (n^3 - n).
Also (n^3 - n) is divisible by 6.
So it can be shared equally....
i think the remaining n.o of gold will b n^4-n^2
n.o of rooms= n
n.o of boxes in 1 room= n
total no of boxes is n^2
n.o of gold coins in 1 box = n^2
total n.o of coins = n.o of boxes * no of coins in 1 box
= n^2 * n^2
remining coins= n^4-n^2
this can be divided by 6 in all cases
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