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Problem 400

Combinatorics Difficulty 2.6 Find the answer Junior Mathematical Olympiad · Netherlands

In a cafe, each product costs at most $12$ ducats. Currently the cafe owner is only using coins worth one ducat. This is unpractical for the more expensive products, however. Therefore, the cafe owner has decided to introduce two types of coins next to the coins of one ducat. He is doing this in such a way that as many values from $1$ to $12$ ducats can be paid with at most two coins (without change).
What is the worth of the two new types of coins?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

$4$ and $6$

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