A neat counting problem from the 1995 AJHME

Stumbled on a neat counting problem tonight on an old math contest. Here’s a link to the 1995 AJHME hosted by Art of Problem Solving:

Problem 23 from the 1995 AJHSME

and here’s the problem:

How many four-digit whole numbers are there such that the leftmost digit is odd, the second digit is even, and all four digits are different?

I thought it would interesting to have both kids talk through the problem just to see if they would take different approaches. It turned out the way they approached the problem was similar, and both were left with the same multiplication problem as the last step. They way the multiplied out the final product was drastically different.

here’s my older son:

and my younger son:

Definitely a nice counting problem, and the difference in multiplying strategies was fascinating to me.

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