- Thread starter Hharouff
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- Mar 16, 2016

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Look at stage 1 and compare to stage 2:

Can you see that in stage 2, 3 more triangles are removed, one on each side of the triangle removed in stage 1?

Now look and compare stage 2 to stage 3:

Again, for each of the triangles removed in stage 2, there are three more removed around it (ie 3x3 = 9) removed in stage 3

For stage 4, each of these 9 will have 3 removed from around it, ie 9x3 =27 removed.

The "triangles removed column" are powers of 3.

Note that the triangles removed = 3 ^ (stage number -1)

So, the number of triangles removed in stage 21 will be 3^20.

Stage number | triangles removed |

1 | 1 = 3^0 |

2 | 3 = 3^1 |

3 | 9 = 3^2 |

4 | 27 = 3^3 |

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Do you know the sum of a