Jane is baking a pizza for herself and two friends to share. The available toppings she has are ham, mushrooms, onions, and pepperoni, plus plain cheese is an option as well.

Halfway through adding toppings, as shown, Jane remembers she wants to be able to cut the finished pizza into three equal wedges, a connected run of 4 slices for each person, so that every wedge has the same toppings in the same amounts. That way she and her friends can each have an equal share.

How many different ways could Jane distribute toppings on the rest of her pizza?

Click the open slices to cycle through toppings, then check to see if your distributions are valid. Or, write a formula or script to determine the answer.