Bag$ of Dollar$
Divide $554 (in whole $ increments) into a number of bags so that I can ask for any amount between $1 and $554, and you can give me the proper amount by giving me a certain number of these bags without opening them. What is the minimum number of bags you will require?
The answer is 10.
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1 solution
You divide $554 (in whole $ increments) into 10 bags as follows:
1, 2, 4, 8, 16, ... , 256, 43.
The first 9 bags contain a total of $511 as per the following series:
20, 21, 22, 23, 24, ... , 28.
To gain a better understand standing, consider the simple case where $12 needs to be divided into a number of bags. You divide $12 into 4 bags as follows: 1, 2, 4, 5. Then,
If I ask for $ [You give $] --> 1 [1] , 2[2] , 3[1+2], 4[4] , 5[4+1] , 6[4+2] , 7[4+2+1] , 8[5+2+1] , 9[5+4] , 10[5+4+1] , 11[5+4+2] , 12[5+4+2+1]