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

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(52778) (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.

RELATED QUESTIONS
1) There exists a 5 digit number N with distinct and non-zero digits such that it equals... (answered by Edwin McCravy)

What is the sum of all the four-digit numbers whose digits are permutations 1,2,3, and... (answered by stanbon)

find a 4 digit number whose first digit is 2 .the second digit is 1 more than the first... (answered by ikleyn)

Find three consecutive odd whole numbers such that the sum of their squares is a... (answered by ankor@dixie-net.com)

Find a four-digit number that satisfies the following: The digits are all different, the... (answered by Edwin McCravy)

find the two-digit number whose units' digit is 5 more than its tens' digit and whose... (answered by Gogonati)

A five digit no whose third digit is one greater than the sum of the first two digits,... (answered by ankor@dixie-net.com)

There is a two-digit number whose digits are the same, and has got the following... (answered by josgarithmetic)