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Digit Sum

Problem

The digits in the number, 42, add to six. There are exactly six 2-digit numbers with this property: 15, 24, 33, 42, 51, and 60.

How many 3-digit numbers exist for which the sum of the digits is six?


Solution

There are exactly twenty-one 3-digit numbers for which the sum of the digits is six:

105, 150, 501, 510
114, 141, 411
123, 132, 213, 231, 312, 321
204, 240, 402, 420
222
303, 330
600

Can you see how this list was produced?
What about 4-digit numbers with this property?
What about numbers below 10000?
Can you generalise for up to n-digit numbers?

Problem ID: 206 (17 Feb 2005)     Difficulty: 1 Star

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