## Leaving 6 diamonds by removing 4 matchstick puzzle

Can you remove 4 matches to leave 6 diamonds in the puzzle figure of eight diamonds made up of matchsticks? No matchstick should be left hanging.

#### The puzzle

In the following puzzle figure, remove 4 matches to leave 6 diamonds.

Each matchstick must be a part of a triangle or a diamond.

**Recommended time to solve** the puzzle is 15 minutes.

### Solution to matchstick puzzle remove 4 matches to leave 6 diamonds: Counting diamonds

Unless you know how to count diamonds or rhombuses, you won’t be able to solve the puzzle. The following figure shows two diamonds joined together, sharing one side and one triangle.

A diamond or a rhombus has two pairs of parallel sides all tilted and all equal. Further—if you join the shorter diagonal, the diamond is divided into two equilateral triangles of equal sides.

In other words, if you join two matchstick triangles (all sides automatically of equal length) along a common side, you get a diamond or rhombus.

The figure above has three triangles but two diamonds. One triangle of sides 3-4-5 is shared by the two diamonds.

**Question is**—how many diamonds does the following puzzle figure have?

To remove confusion, we must devise a system of counting the diamonds that counts accurately and comprehensively.

First, we will count the diamonds horizontally in the top and bottom rows. The top row has horizontally 3 diamonds. And the bottom row also has 3. Two rows combined have 6 diamonds. Is that all?

Besides these six diamonds, the figure has two more diamonds made up of sides 1-2-3-4 and 5-6-7-8. Two pairs of triangles are joined vertically to form these couple of diamonds.

In total then, we have eight diamonds. Our job is to remove 4 matches to leave six diamonds.

In other words, by removing 4 matches we have to reduce number of diamonds by 2.

### Solution to the matchstick puzzle remove 4 matches to leave 6 diamonds: Structural analysis and logical reasoning

As the puzzle figure is symmetric, we may say,

Conclusion 1:We have to remove 2 matches and reduce 1 diamond twice.

It follows,

Conclusion 2:For each pair of matches removed 1 and only 1 diamond must be destroyed.

The second conclusion is important, and it implies,

Conclusion 3:Each pair of matches removed must not affect any other portion of the figure except reducing the number of diamonds by 1.

This hints at **isolated pair of matchsticks, that too two such pairs.**

Previous exercise of counting helps to identify the two check-marked isolated pairs of matchsticks each of which adds only 1 diamond to the total diamond count.

The other six diamonds are too closely joined together for the removal of matchsticks. The solution shown.

The wagon wheel has two diamonds in each horizontal row and two more vertically oriented diamonds. That makes six diamonds.

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