# possible bills one can create with two types of bills

My friend asked me this question, and it's been bugging my mind

There are 5€ bills and 8€ bills, what are all the possible bills one can create with these two types of bills. Prove your answer

the only hint is to use strong induction

How can I approach this question, how can I solve it ?

I think it is related with combination, but I couldn't quite justified it in my mind

Thanks

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One can do it crudely. Try to make various quantities. After a not very long time, you will find $5$ consecutive quantities that can be made. After that, anything larger can be made by adding a suitable number of $5$'s. This is because if you have five consecutive numbers $a$, $a+1$, $a+2$, $a+3$, and $a+4$, then any number $b\gt a+4$ differs from one of these by a multiple of $5$.