# Inspired by Thaddeus

**Discrete Mathematics**Level 4

\[ 3 = 1 + 2 = 2 + 1 = 1 + 1 + 1.\]

The product reduction of a representation, refers to multiplying each of these terms together. For example, we would obtain the values of \( 3, 2, 2, 1 \) respectively. Out of these 4 products, 2 of them are odd and 2 of them are even.

How many odd product reductions of the composition of 10 are there?