Sharing a new problem from Catriona Shearer with the boys

Saw this problem from Catriona Shearer today and just had to share it with the boys when they got home:

Here’s my 7th grader’s solution to the problem:

Here’s my 9th grader’s completely different solution:

As always is is fun to hear kids working through problems – especially the amazing ones from Catriona Shearer!

2 thoughts on “Sharing a new problem from Catriona Shearer with the boys

  1. Quizmanship-based answer. If the picture doesn’t really matter, let’s consider the simple case where the triangle is a right triangle (so one of the three shaded regions disappears). Now one cuts up the picture into 5 pieces, of which 2 are shaded.

    As a mathematician, I’m more interested in the fact that the picture doesn’t matter, than the actual fraction, so this is slightly unsatisfying. But since I’m coaching math competitors these days I’m also practicing looking for such tricks.

    1. I look at puzzles like this and it is hard to set aside my old math contest background. But I do find it fun to hear the solutions my kids come up with since they aren’t involved in any of the math competitions anymore.

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