SOLUTION: how can you make 50 cents with 13 coins?

You must use pennies because 13 nickels is much more than 50 cents.
Since 50 is a multiple of 5, you must either use 5 pennies or 10 pennies.

If you use 5 pennies, then you must make the remaining 45 cents
with 8 coins.  That can be done only with 7 nickels and 1 dime.

If you use 10 pennies, then you must make the remaining 40 cents
with 3 coins.  That can be done only with 1 quarter, 1 dime, and
1 nickel.

So there are two ways:

5 pennies, 7 nickels, and 1 dime, or
10 pennies, 1 quarter, 1 dime and 1 nickel.

Edwin