Question 20
Determine the number of quadruples of integers (not necessarily distinct) between $1$ and $12$ (extremes included) that satisfy all the following conditions:
- the sum of the first two numbers is even
- the sum of the first three numbers is a multiple of $3$
- the sum of the four numbers is a multiple of $4$.
(Two quadruples that differ even only in the order of the addends are to be considered distinct).
- the sum of the first two numbers is even
- the sum of the first three numbers is a multiple of $3$
- the sum of the four numbers is a multiple of $4$.
(Two quadruples that differ even only in the order of the addends are to be considered distinct).