Robbers and a Monkey
A party consisting of seven robbers and a monkey had stolen a number N of nuts,which were to be divided equally among the robbers.In the night a robber woke and decided to take his share.He found that,if he gave 1 to the monkey ,the remaining nuts could be divided in 7 equal lots.He gave one to the monkey and took his share.The other robbers woke in succession ,found that the same thing was possible and each gave 1 to the monkey and took one-seventh of the remaining nuts.In the morning they divided what were left and they found that if they gave one to the monkey the nuts could be divided into 7 equal lots.Let the least possible value of N be M.It shouldn't take more than a minute.:) Enter last three digits of M as your answer.
The answer is 795.
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1 solution
The value -6 of N satisfies the numerical conditions;for -6-1=7, -7/7=-1 , -7-(-1)=-6. Thus -6 is unaltered by the set of operations corresponding to what each robber did.Hence the value of N can is -6+k.7^8 , k belongs to natural number and we get minimum value when k=1.