Jumbled Hopscotch (2-12) [video]

Lately, we’ve seen some lovely hopscotches made by our neighbors in sidewalk chalk for everyone to use, but what would happen if we jumbled the numbers? First, we can ask ourselves: How many ways can we reorganize the numbers in hopscotch? This can be a tough question, so we might want to start with a hopscotch that goes up to 4 or so and then follow the pattern from there. But we can also wonder: Out of all the ways of reorganizing the numbers, how many can we still jump through? If the 1 is too far from the 2, it might not work out! What does this depend on? How many jumpable hopscotches can you make?

Jumbled or not, you can still ask other hopscotch questions, such as: If you add up every number you hopped on, how many ways can you jump through your hopscotch such that your numbers add up to 15? How many different totals can you make? Are there totals that are impossible to make? What about ones that come up a lot? Your answers might be different depending on how jumbled your hopscotch is!