How many ways are there to insert plus signs + between the digits of number 111111 ...111 which includes thirty of digits 1 so that the result will be a multiple of 30?
The total will automatically be a multiple of 3 by its digital root total being conserved, so we need worry only about the sum being a multiple of 10. The number of addends needs to be a multiple of 10, so the number of + signs needs to be one less than a multiple of 10.
You can insert 9, 19 or 29 + signs, and there are 29 places between available for them, only one + or no + between any two 1's.
C(29,9) = 10015005
C(29,19) = 20030010
C(29,29) = 1
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total = 30045016 ways.
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Posted by Charlie
on 2021-05-03 08:52:43 |
solution
