## Remove 3 and move 2 matches puzzle

In the puzzle figure, remove 3 and move 2 matches to form 3 squares equal in size. Each matchstick in the solution must be a part of a square.

**Recommended time to solve** is 10 minutes.

For the inexperienced, this is not an easy puzzle. Do try before going through the solution.

### Solution to the remove 3 matches and move 2 to form 3 squares puzzle: Understanding the problem precisely

We will carry out the number of stick analysis first.

When 3 sticks are removed, 9 matchsticks remain. Target in precision is,

Conclusion 1:To form 3 equal squares with 9 matchsticks.

The maximum number of sticks required to form 3 equal squares is 12 and the most compact 3 square figure shown below has 10 sticks and 2 common matches.

Adding 3 sticks to any of the following two attached squares by conventional means will cause three squares of 10 sticks and 2 common sticks, as shown above.

On a brief look you would find no way to add two matches to the above two square figure and form 3 squares. The two squares have 7 matches and, as specified in the puzzle, you may add 2 matches to it to form the desired 3 square figure.

The core problem is then specified as,

Core problem:Add 2 matches to a 7-match two adjacent square figure and form 3 squares.

### Solution to the remove 3 and move 2 to form 3 squares puzzle: Property change analysis to get over the apparent impossibility and solution

In this apparent impossible task, you would always think of adding the two extra sticks on the **outside of the two squares and not on the inside.** And it is **really impossible to form an additional square on the outside of the two adjacent squares by adding two matches.** To do it, you need 3 matches, not 2.

Urged by the property change analysis technique, the **question** is asked: Can we not add the two matches on the **inside of the two adjacent squares?**

Answer is, **Yes, you can.** And that is the **breakthrough idea.**

The solution is shown.

The two matches added inside are:

- Vertical and placed between the two top and the two bottom sides, one inside the first square, and the other inside the second square.
**Separated exactly by one matchstick length.**

The two sticks added together with portions of the top and bottom sides shared with the existing two squares form the third square equal in size to the two existing squares.

This is the case of **Square in Square technique **where there may be *infinitely many solutions by adding the extra two sticks anywhere inside the first and the second existing square.*

As three equal squares are formed by 9 matches, **there must be 3 common sticks. **These common matchsticks are highlighted in the figure shown.

We have solved the puzzle using no prior experience.

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