# Patterns for Allergic Cliffs and Stone Cold Caves

• So in the early difficulties, the Allergic Cliffs and Stone Cold Caves levels have a discernible pattern - they focus on a combination of one, two or three features that they do/don't like. However on the fourth/ hardest difficulty, I really cannot for the life of me (and the Zoombinis) figure out what they are, or aren't looking for.

What do these two levels focus on, on the hardest difficulty to accept/deny Zoombinis through the level?

• I've found a blog that usefully explores the puzzles, so I'm copying out the results and linking to each one.

As a background, each Zoombini has four categories - hair, eyes, nose and feet - which can have different styles, for instance ponytail, sunglasses, blue nose, propeller.

First, for the Allergic Cliffs on Very Very Hard. There are bridges leading to two cliffs. You need to select which bridge to send each Zoombini across, without the cliff rejecting it. One of the cliffs will pick three styles from three different categories - for instance, it might pick spring feet, one eye and blue noses. That cliff will then reject any Zoombini that has any of those three styles. The other cliff will then reject any Zoombini that doesn't have at least one of those three styles.

https://www.norledgemaths.com/blog/zoombinis-maths-sneezing-cliffs-and-set-theory

Now, for the Stone Cold Caves on Very Very Hard. There are four caves you need to sort the Zoombinis into. A set of two guards will block either the top two or the bottom two, and another set will block either the left two or the right two. First, the categories are evenly split amongst the vertical guards and the horizontal guards - for example, the vertical guards might care about hair and feet whilst the horizontal ones care about eyes and noses. One of the guards in each set will now pick a style for each of their categories that they reject - for instance, if the vertical guards care about hair and feet, one of them might reject scruffy hair and springs. The other guard in the set will then reject all Zoombinis who don't have at least one of those styles. Meanwhile the horizontal guards could have one of them rejecting red noses and sunglasses, whilst the other will reject everyone without either a red nose or sunglasses (or both).

https://www.norledgemaths.com/blog/zoombini-maths-cave-sorting-on-harder-difficulty-levels

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2