At the Hmm… Sessions in November, something cool happened when a couple of the students were showing the rest of us the solution to a puzzle. (Update: Later this year, the Hmm Sessions were renamed “One Hundred Factorial” after the first puzzle we ever did.)

(For those who don’t know, The Hmm… Sessions are a regular gathering that I run where staff and students solve puzzles together in a group.)

The puzzle was this one from the AustMS Gazette November 2010:

Three boxes are on the table. One has red balls, one has blue balls, and one has balls of both colours. Three labels are made for the boxes, but they are misplaced so none of the boxes are labelled correctly. How many balls would you need to retrieve from the boxes in order to determine the correct labelling?

Well, as I said, a couple of the students were showing us their solution to this puzzle at the big whiteboard. As they were doing this, each person watching cried, “Oh! That’s cool!” in turn. Each of us came independently to a sudden realisation of how the solution worked — we had “seen” the solution before it was actually presented.

I think this is very cool because it says to me two things about how mathematicians work:

One: Mathematicians don’t really listen fully to other mathematicians. Our minds are always racing ahead making connections and figuring things out on our own. Perhaps this is because we get the most thrill from seeing things ourselves rather than being told.

Two: Mathematicians come to understanding at their own pace, which may be fast or slow. At the Hmm… sessions, each of us had our Aha momentat a different time.

Apart from these two, the other thing that really impressed me was that none of us looked down on anyone else for taking longer but merely rejoiced when someone did see it. I couldn’t hope for a better atmosphere in the Hmm… Sessions than that!