Jada has 1 penny, 2 nickels, and 1 dime. How many different sums of money can she make, if she uses at least one coin?
This brainteaser was supplied by the Mathematical Olympiads for Elementary and Middle Schools (www.moems.org).
Solution: 9 sums .
At most, she can make 1 + 5 + 5 + 10 = 21 cents, if she uses all four coins. The question is, which amounts less than 21¢ are possible?
If she uses the penny in a combination, she can make any value that ends in 1 or 6. If she does not use the penny, she can make any value that ends in 0 or 5. The complete list of possible sums is shown below:
1=1 ; 5=5 ; 5+1=6 ; 5+5=10 ; 10+1=11 ; 10+5=15 ; 10+5+1=16 ; 10+5+5=20 ; 10+5+5+1=21.
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