Someone on the Q&A page asked me to do one of these “point A to point B” questions, so I figured I’d try to come up with one worthy of being called a challenge question. I think this is a bit easier than the usual. I expect someone to get it pretty quickly.

Please note: This is the first Challenge I’ve posted since I made some slight changes to the commenting policy on this blog. If you don’t have a Disqus account with a verified email address, your comment will not appear on the site immediately. Don’t freak out—I get an email for every comment that’s posted. I will still be able to tell who responded correctly first, so I’ll know who to award the Math Guide to. As always, the usual contest rules apply.

Joss is playing an elaborate version of the game everyone plays as a kid where the floor is lava and you can only step on pillows*. In Joss’s version of the game:

  • The pillows are laid out in a pattern just like the one in the figure above
  • Joss can only move the way a knight in chess moves (so his first move will put him 1 diagonal space away from a red corner)
  • Any pillow he lands on disappears when he leaves it (assume he leaps directly to the pillow his move would end on, and does not touch other pillows in between)

If Joss begins on the center pillow, and makes the minimum number of moves necessary to land on each red pillow before leaping to safety on the couch, how many pillows will remain?

*I know not everyone has played this game. Hopefully, even if you haven’t, you can picture the scene.

First correct answer in the comments wins! Good luck.

UPDATE: Props to Peter, who got it first. Solution below the cut.


I’ve never posted a video here before (which is saying something considering that between this main blog and the Q&A Tumblr I’m well over 1500 posts) but this question really seemed to lend itself better to a video explanation than a written one.

I didn’t want to re-record the whole thing to fix this, but note that even though I described a knight’s movement as “up two, over one,” I am aware that a knight can also move down. Anyway, here’s the solution: