## 2 large 1 small triangle puzzle

In the puzzle figure of two small triangles and one large triangle, move 3 matches to form 2 large and 1 small triangle with no hanging stick.

**Recommended time to solve** is 5 minutes.

### Solution to the puzzle move 3 matches to form 2 large and 1 small triangle

Intuitive solution may take a few minutes, but we will solve the puzzle by analytical reasoning.

Total number of sticks in the three independent triangles is 12. First conclusion from common matchstick analysis,

Conclusion 1:To form the two large triangles and one small triangle with 12 sticks, (6+6+3) -12=3 matchsticks must be common between the triangles.

The second conclusion also follows easily,

Conclusion 2:We already have one large triangle and two small triangles. We need to create just one more large triangle by moving the three sticks of an existing small triangle. That will be the most convenient option.

Most important conclusion made now is,

Conclusion 3:As the new large triangle must be of 2-stick side length, one of the 2-stick sides of this triangle forming the two common sticks must be obtained from some part of the existing large triangle.

With this awareness, we identify the check-marked two sides of the existing large triangle as the most suitable two sides of the new large triangle. This is shown in the figure.

Solution is just a step more and is shown.

As the small triangle on the left of the puzzle figure is attached to the mid-point of the 2-stick side of the large triangle, this portion could not be used for getting a contiguous 2-stick side of the new triangle. This is why this small triangle on the left is the ideal one to provide all the three sticks to be moved.

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