In matchstick figure, remove 3 matches and leave 3 triangles. You have 10 minutes to solve the puzzle. Try and then learn how to solve from solution.

### Remove 3 matches leave 3 triangles matchstick puzzle

In this matchstick triangle puzzle, remove 3 matches from the matchstick triangle figure shown below so that exactly 3 triangles are left.

There must not be any other closed shape, and every matchstick must be a side of a triangle.

**Recommended time to solve:** 10 minutes.

Many triangles in the puzzle figure may confuse you, but let us assure: this is not a difficult puzzle. Try to solve the puzzle first.

### Solution to remove 3 matches and leave 3 triangles matchstick puzzle

The puzzle figure is shown again for the convenience of explanation.

Let us first analyze the number of matches against the number of triangles in the final solution figure.

**Analysis: **The starting number of matches is 13. After removing 3 matchsticks, the number of matches would reduce to 10. To make 3 equal sized triangles, you would need a maximum 9 matches. So you can conclude,

Conclusion 1:The three triangles in the final figure cannot of same size.

It follows,

Conclusion 2:Each triangle formed by matchsticks in the solution has to be equilateral with the length of all sides equal. So, the solution figure must have one large triangle of side length 2 matches comprising 6 matches and two smaller triangles with a side length 1 match comprising 3 matches each. The total number of matches 12 exceeds 10 available matches. So, 2 matches must be common between the triangles.

This is a **clear specification of the solution figure.**

It is time now to figure out how one large and two small triangles can be formed by removing three matchsticks.

The key idea is,

Key idea:The matches are not moved, but removed.

So a key conclusion made,

Conclusion 3:The single large triangle and two smaller triangles must already be existing in the puzzle figure.

At this point of time only, we look closely at the puzzle figure to find two large triangles staring at us.

Remove either the smaller triangle A formed by sticks 1, 2, and 3 or the smaller triangle B formed by the sticks 3, 4 and 5 to get one large triangle and two smaller triangles formed by 10 matchsticks.

Following figure represents the two possibilities.

There would be two possible solutions. But if you flip one solution vertically you’ll have the second. So rotationally unique solution is only one.

One of the solutions is shown. The three sticks removed are kept faded out and sticks of large triangle colored red.

#### End note

Observe, we never really attempted to solve the puzzle from the actual puzzle figure till we could form a clear idea about the nature of the puzzle figure. But then, forming the final figure turned out to be dead easy at that stage.

This analytical approach is rather general and has the call name of Systematic problem solving. No randomness in this approach at all.

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