A short introduction Cookie policy

Solution to: The King's Gold

A fair division of the coins is indeed possible. Let the number of rooms be N. This means that per room there are N chests with N coins each. In total there are N×N×N = N3 coins. One chest with N coins goes to the barber. For the six brothers, N3 - N coins remain. We can write this as: N(N2 - l), or N(N - 1)(N + l). This last expression is divisible by 6 in all cases, since a number is divisible by 6 when it is both divisible by 3 and even. This is indeed the case here: whatever N may be, the expression N(N - 1)(N + l) always contains three successive numbers. One of those is always divisible by 3, and at least one of the others is even. This even holds when N=1; in that case all the brothers get nothing, which is also a fair division!

back to the puzzle

Copyright © 1996-2016. RJE-productions. All rights reserved. No part of this website may be published, in any form or by any means, without the prior permission of the authors.
This website uses cookies. By further use of this website, or by clicking on 'Continue', you give permission for the use of cookies. If you want more information, look at our cookie policy.Continue