SOLUTION: Randy writes down a 5-digit number whose digits are all different, and whose first digit is the sum of the other four digits. How many 5-digit numbers are there with this property

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Question 1121619: Randy writes down a 5-digit number whose digits are all different, and whose first digit
is the sum of the other four digits. How many 5-digit numbers are there with this property?
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.
The digits following after the very first digit are 0, 1, 2 and 3 and all their permutations.


Notice that the sum  0 + 1 + 2 + 3 = 6 is less than 10,  


while  1 + 2 + 3 + 4 = 10,  so the digits  1, 2, 3 and 4,  starting from 1, do not satisfy the condition.


Therefore, you have  4! = 24  options by making permutations of the digits  0, 1, 2 and 3  in the 2-nd, 3-rd, 4-th and 5-th positions.


In the very first position you have the digit 6 in all cases.

Solved.