Question 1
A positive integer is *happy* if
* all of its digits are different and non-zero,
* one of its digits is equal to the sum of the others.
For example, $253$ is a happy number. How many happy numbers are there?
* all of its digits are different and non-zero,
* one of its digits is equal to the sum of the others.
For example, $253$ is a happy number. How many happy numbers are there?