The basic problem, if you don’t know it, goes like this: At McDonalds you can order Chicken McNuggets in boxes of 6, 9, and 20. What is the largest number such that you can not order any combination of the above to achieve exactly the number you want? (Wording lifted frommathproblems.info, by Michael Shackleford.) I reworded a little bit, adding a bit about how it “used to be” this way, but now McDonald’s offers different nugget options. I gave this problem to all three Advanced Algebra classes in the week before winter break, and had three very different experiences.

In one class, they ate it up. This class usually has a hard time with rote work, but loves discussing ideas. They loved taking a long patient look at this problem. In another class, half of them were excited to get to the bottom of the puzzle, and some of them requested a square 100-integer grid to help them organize their thoughts. In the third class, the one with the ‘highest performing’ students, where, if every day consisted of a new drill, they’d be happy didn’t do so well. It was as if I hadn’t posed the problem. They simply shut down, and turned the class into social hour.

I was invigorated, perplexed, and completely deflated at different times, a bit surprised at the sources of those feelings, and plenty interested in figuring out how to meet each class where they are and run for the rest of the year.

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Only tangentially relevant, but this problem is also used in the MIT open course for intro to programming. I’ve just started working on a Python program to solve this.