# Matches

### Counting matches

To count matches, we usually group them by 10.

As I'm a little mad, I group them by 13, and remains 7 matches.

If I group them by 7, remains 5 and last if I group them by 5 remains 2.

Knowing I surely have less than 500 matches, how many ?

Solution
### Chinese remainder extension

Same question, If I group by 12 remains 7,
by 10 remains 5 and by 9 remains an even number.

I surely have less than 200, but how many ?

Solution
Details

And also :

### Too easy...

Same question, If I group by 12 remains 5,
by 10 remains 5 and by 9 remains also 5.

I still have less than 200 (but more than 5 !) , how many ?

Solution