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

 

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