What is the largest amont of money, obviously in coins each
less than one dollar, you can
have and not be able to make change for a dollar?
Using the example as a starting point
Consider 3 quarters and 3 dimes. You have $1.05 but you can not make change for a dollar.
First thoughts:
I thought of initial constraints on each coin less than one dollar
3 quarters can not make change for a dollar ($.75)
9 dimes can not make change for a dollar ($.90)
19 nickels can not make change for a dollar ($.95)
99 pennies can not make change for a dollar ($.99)
Possible methods
Algebra?
.25Q + .10 D + .05 N + .01 P < 1
If Q =3, then D < 5.
Trial and error method?
This worked for me.
More definitive.
What combinations of coins will give the maximum?
The highest amount of money I got was $1.19
3 quarters + 4 dimes + 4 pennies = $1.19
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