Last year, while reading and writing about cognitive load theory, I came across something weird that I couldn’t explain. A paragraph from Greg Ashman’s latest reminds me of this puzzle. It’s really small and inconsequential, but it’s been bugging me. Maybe you can figure it out.

He writes:

One of my PhD supervisors did an experiment in the 1980s. Undergraduates were given as series of problems. Each problem involved a starting number and a goal number. The participants had to get from the first number to the second using only two moves which they could repeat: **multiply by three or subtract 29**. The problems were designed so that each one was solved by alternating the steps. Although the students could generally solve the problems, very few ever worked out the rule.

Great. Multiply by three, or subtract 29.

Except you go back to that paper, and it’s actually subtract 69.

Where did Greg get the “subtract 29” from? I don’t know, but it could be from this piece by Sweller in 2016.

Anyway, totally unimportant. Completely uninteresting. But. Did he forget? Was it a typo? Did he decide — as so many before — that 69 is a funny number to talk about in classes?

If you see me and I’m looking pensive, this is probably what I’m thinking about.

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First I wondered if it’s possible that it doesn’t matter what you subtract. Then I looked into a few combinations and got stumped with one. Now I’m wondering what the rules are for setting up the rules. What conditions must be true about the factor and the difference? What conditions must be true about the starting number and the target? Talk about an open-ended problem…

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Ooh! Great problem finding. I love it.

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