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The sum of the last four digits of Marian’s phone number is 30.  How many such four-digit sequences are there?

 Nov 1, 2019
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This is a partitions problem in 4 parts:
9 + 9 + 9 + 3 = 30...........4 permutations
9 + 9 + 8 + 4 = 30...........12  
9 + 9 + 7 + 5 = 30...........12
9 + 9 + 6 + 6 = 30...........6
9 + 8 + 8 + 5 = 30...........12
9 + 8 + 7 + 6 = 30...........24
9 + 7 + 7 + 7 = 30............4
8 + 8 + 8 + 6 = 30...........4
8 + 8 + 7 + 7 = 30...........6
If you add up all the permuations, you should get =84

 Nov 1, 2019

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