PROBLEM #6 SOLUTION
I have divided $547 into bags of different whole dollar amounts such that you can ask me for any
whole dollar amount from $1 to $547 and I can provide you with that exact amount by
combining my bags of money AND without open any of the bags to transfer money.
What is the minimum number of bags required to fulfill this task?
Solution:
You divide $547 (in whole $ increments) into 10 bags as follows:
1, 2, 4, 8, 16, ... , 256, 36.
The first 9 bags contain a total of $511 as per the following series:
20, 21, 22, 23, 24, ... , 28.
To gain a better understanding, 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 $:
1 2
3
4
5
6
7
You give $:
1 2 1+2 4 4+1 4+2 4+2+1
8
9
10
5+2+1 5+4 5+4+1
11
12
5+4+2
5+4+2+1