This level was undoubtedly one of my favourites when I played the game as a child, and is responsible for many pizza-related sayings in my house. Unlike the previous two levels, this one is not focused at all on Zoombini characteristics. Instead, the player is tasked with creating the perfect pizza for some very picky tree trolls. When each troll has had their pizza made, they move out of the Zoombinis' way, allowing to group to continue.
On the first level, players have to create a pizza for a single troll, Arno, from a choice of five different toppings. It's a little unclear what some of the toppings are, so I've taken a best guess at names. To create a pizza, the player selects one or more desired toppings from the machine on the left, then presses the large pizza button at the top. The pizza is transported over Arno, who either flings it on the rock behind him if the pizza is OK but missing something, or in the pit to the front if there's something on it that he doesn't approve of. On Not So Easy, the player gets six attempts before Arno starts hitting his pizza-delivery Zoombinis off the screen and back to Zoombini Isle in frustration.
It's also OK to introduce a new topping each time. In the example below, once I had figured out that Arno liked mushrooms and salami (but not cheese), I knew that these two ingredients would have to be on his perfect pizza anyway, so included them in my tests of chilli and pineapple.
The next difficulty level introduces an extra troll, Willa, and some extra choices for the pizza machine. Cheese is removed, but is replaced with two ice-cream sundae options, namely sprinkles and a cherry. Essentially, both still function as "pizza toppings", giving the player a choice of six toppings in total and doubling the number of possible unique pizzas to 64.
As before, the player has sufficient attempts (seven on this difficulty setting) to try each topping on its own, then combine to create both trolls' perfect pizzas. There is never any overlap between the two trolls - for example, they will never both like mushrooms. However, there is no guarantee that all of the toppings will be used, and the trolls frequently both reject one or two toppings.
The third difficulty level introduces a third troll, Shyler, and cheese appears once again on the pizza machine. A choice of seven toppings now means that there are 128 possible unique pizzas, making guessing correctly nearly impossible. However, with eight pizza attempts before your Zoombinis end up getting smacked around, the tactic of producing single-topping pizzas still works every time.
It's at Very Very Hard that the puzzle changes subtly, so the algorithmic approach breaks down and alternative tactics are needed. Because of these greater complications, I've saved this for a separate post, as this one was getting too long!
- Get pupils to work out or list the total number of pizza combinations for each level of difficulty - a great opportunity for some systematic listing and pattern spotting.
- Create Pascal's Triangle from the pizza choices - explore the link between the number of available toppings and the number of unique pizza combinations.
- Explore different strategies for solving each problem - as yet, I've not found a more efficient algorithm than the one described above - but there may be one!