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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.

Move 2 Matches to Make 3 Triangles Matchstick Puzzle graphic

Time to solve: 5 minutes.

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

Instead, we’ll take a systematic problem solving approach to solve the puzzle using step by step reasoning.

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

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 only one triangle and create two new additional triangles.

It is an 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 and 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 match 1 and 2, the solution is achieved easily and naturally.

Move 2 Matches to Make 3 Triangles Matchstick Puzzle solution

End note

The solution is directly staring at you, so to say. It is so natural. Instead of directly pointing out the solution, as is our habit, we have gradually moved towards the solution by step by step reasoning.

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