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 just 3 matches from the matchstick triangle figure shown below so that exactly 3 triangles are left. There must not be any other closed shape, as well as every matchstick must form a side of a triangle.

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

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

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

The puzzle figure is shown again for convenience of explanation.

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

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

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

As each triangle formed by matchsticks in the solution has to be equilateral with length of all sides equal, there has to be,

Conclusion 2:One large triangle of side length 2 matches that consumes 6 matches and two smaller triangles with side length 1 match consuming 3 matches each. The total number of matches needed 12 exceeds 10 available matches. So there must be 2 matches common between the triangles.

We have the **clear specification of the solution figure** this quick.

It is time now to figure out how one large and two small triangles can be left out.

The key idea is,

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

So a key conclusion is confidently 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 and find two large triangles staring straight at us. You remove either the smaller triangle A formed by sticks 1, 2, 3 or the smaller triangle B formed by the sticks 3, 4 and 5 and you would have 1 large triangle and 2 smaller triangles left with 10 matchsticks.

Following figure represents the two possibilities.

There would then 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 that 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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