Men, monkey and coconuts problem

Five men and a monkey collected a heap of coconuts in a desert island. The men went to sleep in the night. One of them got up in the middle of the night and divided the heap into five equal parts and found an extra coconut, which he gave to the monkey. He hid his share and made one heap combining the rest of the coconuts. Then, the second person got up and divided this new heap into five equal parts and again found an extra coconut, which he gave to the monkey. He also hid his share and made a new heap of the remaining coconuts. This process continued until the last person did exactly the same thing as the others. What must be the minimum number of coconuts in the original heap if

(a) the next morning when they divided the last remaining heap into five equal parts, there was no coconut left for the monkey.

(b) the next morning they divided the last remaining heap into five equal parts, they again found an extra one, which they gave to the monkey.

Cheers,

Nalin Pithwa.

PS: One good way to increase concentration, motivation, intellectual stamina for solving such demanding puzzles or math problems for the IITJEE or RMO/INMO or even Mensa challenges is to give yourself a “reward” after you actually solve that problem. So, you may go ahead and have chilled coconut juice after you solve this puzzle. Anyway, these are the hot summer days in India.

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