Based on the question Eight coins for the fair king:
I saw a comment saying "There isn't a good solution known even with three coins in all cases".
So the challenge here is to try to solve the same problem placed above, except with only 3 coins.
The rules are:
You must create 3 coins of different value, no more.
Any sum of money must be paid with only 3 coins. This sum should be paid without giving change.
You must set N such that no price is allowed to be greater than N.
I've tried to solve it myself and the best combination I could get to was
5, which can get me to a maximum of N = 12.
The highest number that follows the rules wins, and if there's proof that it's definitely the highest answer possible, it gets the tick.
Note: You may only use up to 3 coins to pay every amount, rather than 8.