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Sum of 10

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Hi Max: Can this question be solved algebraically? I know it can easily be solved by writing a short code in Phthon or C or Java....etc. How many 10-digit integers have the SUM of their digits be multiples of 10? Example:1123769146 =1+1+2+3+7+6+9+1+4+6==40 - which is mutiple of 10. Thanks very much.

 May 14, 2022

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This is equivalent to finding the number of solutions to the nine linear Diophantine equations \(a_1 + a_2 + a_3 + \cdots + a_{10} = 10, 20, 30, \cdots, 90\), You can do that using stars-and-bars method, but it will be very tough.

 May 14, 2022
edited by MaxWong  May 14, 2022

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