# Task No. 3.1

## Condition:

Polina makes jewelry on order for a jewelry store. Each piece of jewelry consists of a chain, a stone, and a pendant. The chain can be silver, gold, or iron. Polina has stones - a diamond, an emerald, and a quartz - and pendants in the shape of a star, a sun, and a moon. Polina is only satisfied when three pieces of jewelry are laid out in a row from left to right on the display according to the following rules:

- There must be a piece of jewelry with a sun on an iron chain;
- Next to the piece of jewelry with a sun, there must be a gold and a silver piece of jewelry;
- The three pieces of jewelry in the row must have different stones, pendants, and chains.

How many ways are there to make Polina satisfied?
# Answer: 24

Exact match of the answer - 1 point

## Solution.

Notice that the iron ornament with the sun is definitely in the middle, as it must be between the gold and silver ornaments. For the first position, we can choose a silver or gold chain. After choosing a chain for the first position, the chain for the third position is uniquely determined. For the first position, we can choose the moon or the star. After choosing a pendant for the first position, the pendant for the third position is uniquely determined. The three stones can be arranged in six ways (one of three stones on the first position, one of the remaining two on the second position, and the remaining stone on the third position). There are four ways to correctly arrange the chains and pendants, and for each of these four ways, there are six ways to arrange the stones. In total, $2 * 2 * 6 = 24$.

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