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Move 2 Matches to Make 3 Triangles Matchstick Puzzle

Move 2 Matches to Make 3 Triangles Matchstick Puzzle

In puzzle figure, move 2 matches to make 3 triangles with no match unattached to any triangle. Solve in 5 minutes. Learn how to solve easily from solution.

Move 2 Matches to Make 3 Triangles Matchstick Puzzle

Move just 2 matchsticks in the puzzle figure below leaving exactly 3 triangles. Not a single matchstick should remain unattached to a triangle.

Puzzle Move 2 Matches to Make 3 Triangle

Time to solve: 5 minutes.

You may spot the solution in 10 seconds flat. It is possible.

But we'll take systematic problem solving approach and solve the puzzle using step by step reasoning.

Solution to the matchstick puzzle move 2 matches to make 3 triangles

We'll show the puzzle figure again for convenience.

Move 2 Matches to Make 3 Triangles Matchstick Puzzle graphic

The puzzle figure has two triangles, a small triangle inside a larger one sharing two matchsticks on their bases.

If you move any matchstick at least one triangle will be destroyed. So we conclude,

Conclusion 1: To create 1 more triangle by moving 2 matches, we must destroy one and only one triangle and create two new triangles.

It is accounting of matches moved, triangles destroyed and triangles to be created.

It means,

Conclusion 2: Both matches must be moved from the same triangle not overlapping with the second triangle at all.

From which of the two triangles should we select the two matches to move?

Can we move any matchstick of the larger triangle?

No we cannot. If we do, there would be no way to restore the large triangle as well as create two new triangles with one remaining stick move.

So we make the next conclusion,

Conclusion 3: Both matches to be moved must be selected from the smaller triangle, that too not overlapping with the larger triangle.

The four candidate matchsticks for moving are marked 1, 2, 3 and 4 in the following figure. We are now very near to the solution.

Move 2 Matches to Make 3 Triangles Matchstick Puzzle labeled match candidates

Mentally trying briefly, both the matches 3 and 4 are eliminated as possible candidates for solution.

Finally when we turn our attention to matches 1 and 2, solution is achieved easily and naturally.

Move 2 Matches to Make 3 Triangles Matchstick Puzzle solution

End note

The solution is directly looking at you so to say. It is so natural.

Because of our fondness of exploring how the possibilities can be narrowed gradually down to a single option, we have spent the time in the systematic step by step problem solving.


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