Counting Crayons

There are fourteen crayons in a box. Some are red and some are blue. There are more red crayons than blue crayons. What combinations of red and blue crayons could be in the box?

What generalizations can you make about the combinations of numbers that add up to 14? Are they always even? Are they always odd?

What if the box had fourteen crayons that were red, blue or green. There is at least one crayon of each color. Most of the crayons are red. The least number of crayons is green. What combinations of red, blue and green crayons could be in the box?

What generalizations can you make about the combinations of numbers that add up to 14? Are they always even? Are they always odd?

Adapted from Investigations.

Extension:
Consecutive Odds and Evens: Determine a rule that relates arithmetic operations on four consecutive odd and even numbers.