SOLUTION: You have 15 cookie jars containing 1,2,3,........,15 cookies respectively.you give Amar the permission to take any subset of the jars and remove the exact same number of cookies fr

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Question 1093552: You have 15 cookie jars containing 1,2,3,........,15 cookies respectively.you give Amar the permission to take any subset of the jars and remove the exact same number of cookies from each of the jar he selected.what is the minimum no. of moves in which Amar can empty out all the cookie jars?Justify your claim
Answer by greenestamps(13206) (Show Source):
You can put this solution on YOUR website!

This problem can be solved using binary (base 2) numbers. In binary, the number 15 is

(1*2^3 + 1*2^2 + 1*2^1 + 1*2^0 = 8+4+2+1 = 15)

Amar can empty all 15 jars in 4 moves, but not in any fewer number. There are several ways he can do it; one is shown below.

(1) Take 8 cookies out of every jar that contains at least 8 cookies.
(2) Take 4 cookies out of every jar that still contains at least 4 cookies.
(3) Take 2 cookies out of every jar that still contains at least 2 cookies.
(4) Take the last cookie out of every jar that still contains a cookie.

The numbers of cookies in each jar at the beginning, and after each step are the following: