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Monkeys and Coconuts w/unknown variables (Posted on 2005-05-08) Difficulty: 3 of 5
This is a variation on a classic number theory problem, originally submitted by Ravi Raja here.

There are n men and k monkeys shipwrecked on an island. The men have collected a pile of coconuts which they plan to divide equally among themselves the next morning. Not trusting the rest of the group, one of the men wakes up during the night and divides the coconuts into n equal parts leaving k left over, which he gives to the monkeys. He then hides his portion of the pile. During the night, each of the other men does exactly the same thing by dividing the pile he finds into n equal parts leaving k coconuts for the monkeys and hiding his portion. In the morning, the men gather and split the remaining pile of coconuts into n parts and k is left over for the monkeys. What is the minimum number of coconuts, C, the men could have collected for their original pile?

See The Solution Submitted by yocko    
Rating: 4.4444 (9 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 2 of 10 |

M = Number of men, M > 2
K = Number of monkeys, 1 <= K < M
C = Minimum number of coconuts

Then C = [M^(M+1)] - K*(M-1)

I arrived at that equation by running a program and finding a simple formula that fits. I didn't look at the other solution(s) - honest !!

M=3 K=1: C=79
M=3 K=2: C=77
M=4 K=1: C=1021
M=4 K=2: C=1018
M=4 K=3: C=1015
M=5 K=1: C=15621
M=5 K=2: C=15617
M=5 K=3: C=15613
M=5 K=4: C=15609
M=6 K=1: C=279931
M=6 K=2: C=279926
M=6 K=3: C=279921
M=6 K=4: C=279916
M=6 K=5: C=279911





Edited on May 8, 2005, 7:58 pm
  Posted by Penny on 2005-05-08 19:54:43

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