Math CentralQuandaries & Queries


Question from Mari:
a large shaded triangle changes each day with a white triangle appearing
in the center of each shaded one. If this pattern continues, how many white
triangles will be there on the 6th day? On the 6th day, what fraction of the large outer triangle will be white?THANKS!


I presume that the white triangle has half the edge length and the opposite orientation so it leaves three shaded triangles, each the same size as the white triangle? Then on the next day each of the three shaded triangles is broken up the same way?


For the first question: Draw sketched for the first few days and look for a pattern.
For the second one: It may be easier to figure out what proportion is shaded, then subtract from 1.

Good Hunting!


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