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December 2018 - Math Problem

This triangle has 4 dots on each side. A total of 9 dots were used to make the triangle.

Nine dot triangle

The bottom triangle has 6 dots on each side. A total of 15 dots were used to make the triangle.

Fifteen dot triangle
How many dots, in total, would be used to make a triangle with 10 dots on each side?

Solution:

One possible strategy: 10 dots on each side but 3 overlap, so there are 27 total dots.

How many dots, in total would be used to make a triangle with 12 dots on each side? What about 100 on each side? Can you make a triangle in this way with a total of 56 dots? How do you know?

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