Question

What is the greatest four-digit integer that meets the following three restrictions ?

All of the digits are different.
The greatest digit is the sum of the other three digits.
The product of the four digits is divisible by 10 and not equal to zero.

Answer 1

the lead digit should be 9
to be divisible by 10 , two of the digits must be 5 and 2 , or 5 and 4
We can rule out 5 and 6, and 5 and 8, since the sum would be greater than 9

let's try 952X, X must be 2, but all digits must be different
let's try 9540, no good, since we can't have a product of all the digits being zero

ok, how about the lead digit being 8
then we need 8521, yup, that's the one