1. The price of one pencil is a whole number of eurocents. The total price of 9 pencils is greater than 11, but less than 12 euros, while the total price of 13 pencils is greater than 15, but less than 16 euros. How much does one pencil cost?
Solution. Let $x$ be the price of the pencil in eurocents. Then from

$$
1100<9 x<1200
$$

it follows that $122<x \leq 133$, and from

$$
1500<13 x<1600
$$

it follows that $115<x \leq 123$. But, $x$ is an integer, so from $122<x \leq 133$ and $115<x \leq 123$ it follows that $x=123$ eurocents.