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Math Break: Legos and Trains

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Here’s a Duplo train set:


Its brightly-colored (and rainbow-ordered!) numbered blocks 1-9 fit exactly onto three train cars, with the 10 sitting by itself. Once the adult gets bored assembling the train in the “correct” way for the millionth time just so their toddler can quickly disassemble it and scatter the pieces about, the adult probably wants to have a new system.

What are other ways that the numbered blocks can fit on the trains, with one left over, that makes some sort of ordered sense?

For example,

  • 1,9,10; 2,6,8; 3,4,7 (addition; 5 is left over)
  • 9,6,3; 10,8,2; 5,4,1 (subtraction; 7 left over)
  • 2,4,8; 3,6,9; 1,5,7; (multiples and primes, 10 left over)

I recognize that addition and subtraction are basically the same thing in this case, as would be multiplication/division (although I don’t think it’s possible to do through these blocks).

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