June 24, 2021 Incubator

Daniel and Mason presented on Smileys. That’s a puzzle that has you sparsely filling a grid with smiley faces. Then you start the app running. At each time-step a grumpy face turns into a smiley face if it touches two or more smiley faces.

The initial problem: What are the fewest number of smiley faces needed so that the whole canvas gets filled?

The incubator problem: What are the greatest number of steps needed to fill the canvas?

The app: https://www.jrmf.org/digitalapps/smileys

Incubators happen on Thursdays every week 9:00 PT; 12:00 ET. They are a joyous collaboration of educators and mathematicians.