Question 1191841: A person has 4 coins if different denominations. What is the number of different sums of money the person can form?
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A person has 4 coins if different denominations. What is the number of different sums of money the person can form?
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2^4 - 1 = 15
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Call them A, B, C & D
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A, B, C or D ---> 4
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AB, AC, AD, BC, BD OR CD = 6
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ABC, ABD, ACD, BCD = 4
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ABCD = 1
----> 15
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If any of the coins is equal the sum of any combinations of the others, eg, if D = A + C, then the # of sums is less than 15.
I don't know of any coins where that would apply, but there are a lot of different currencies in the world.
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
We will assume that the denominations are not such that the sum of two of the denominations is equal to another of the denominations; having a system of coinage like that would not make sense.
So we have 4 different coins. In making a sum of money from those coins, we can either choose to use or not use each of the 4 coins. The number of combinations we can make is then the total number of choices we can make. 2 choices for each of the 4 coins means a total of 2^4=16 choices.
So we can make a total of 16 different amounts of money using the 4 coins.
Of course, one of those amounts is 0 -- if we choose not to use any of the coins. So if by "different sums of money" you are meaning non-zero amounts, then the answer is 15 instead of 16.
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