## Move 3 matches to create 5 squares puzzle

In the puzzle figure, move 3 matches of 6 squares to create 5 squares. No matchstick should be kept hanging. Do give it a try.

#### The Puzzle

Move 3 matches of the 6 square puzzle figure below to create 5 equal squares with each matchstick as part of a square.

**Recommended time to solve** is 12 minutes.

Try to solve yourself before going through the solution.

### Solution to the puzzle move 3 matches of 6 squares to create 5 equal squares: Matchstick count analysis and visualization of solution figure

Especially for puzzles on matchstick squares, we do matchstick count analysis at the start.

The six squares are made up of 20 matches. Target is to make 5 squares from these 20 matches. The target figure won’t have then any single common matchstick. **All matches will be used up as sides of 5 independent squares.**

#### Solution to the puzzle move 3 matches of 6 squares to create 5 equal squares: Focus on common matchstick elimination

For explanation, we will use the following figure.

The six square figure has 20 matches and 4 common matchsticks. In 3 moves we will have to eliminate all 4 common matches and automatically will get the solution.

On brief examination, the marked stick of square B is identified as the **most promising stick to move.** If you move this single stick,

**Three common sticks are eliminated at one stroke**, and- No hanging stick is created.
- One square is destroyed.

*This must then be the stick to be moved under any circumstances.*

By moving two more sticks then,

- One square must be destroyed,
- One remaining common stick must be eliminated, and
- With three free moved sticks one new squares must be created without any common stick.

By moving the most promising side stick of square B, the **three squares A, C, and D are left corner-connected with no common stick between the three.** Our work on this part of the puzzle figure is then finished. Now it is time to work on squares E and F.

The other two sticks to move must belong to these two squares. Also, the only common stick remaining is the stick between squares E and F. if we eliminate this common stick by moving two matches we will get our solution.

If we think from a functional point of view,

Conclusion 1:The rest two stick moves should destroy one square and create one hanging stick that can be used as the base of the new square.

#### Solution to the puzzle move 3 matches of 6 squares to create 5 equal squares: Sticks to move identified

Based on all the reasoning, the three sticks to move are identified and marked, as shown.

The solution figure will be as shown.

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