## Move 3 sticks to form six squares puzzle needs an inventive approach

In the puzzle figure of 5 matchstick squares, move 3 sticks to form six squares. No matchstick should be hanging. Each should be a part of a square.

**Recommended time to solve** 15 minutes.

It needs innovative thinking. Do give it a try.

### Solution to move 3 sticks to form six squares matchstick puzzle: Count of sticks and common stick analysis

Total number of sticks in the puzzle figure is 16 with four common sticks of the central square.

To form six independent squares, 24 sticks are needed. That means, if six squares are formed with the existing 16 sticks, 8 sticks must be common sticks.

How is it possible?

Let us examine the most compact six square figure with the maximum number of common sticks as shown.

Number of common sticks is 7, not 8, and so the number of sticks is 17 not 16. We must form six squares with one less stick and one more common stick. This is apparently impossible.

#### Solution to move 3 sticks to form six squares matchstick puzzle: Property change analysis technique applied

When the problem seems apparently impossible to solve, the use of the property change analysis technique often provides a solution.

This technique urges us to list out all the properties of the main element of the problem and imagine exhaustively how each property can be changed for solution. The property listing must be exhaustive including each property that we take for granted and do not consider for manipulation.

It is all about asking persistently—*what is it we assume about the solution figure as taken for granted and unchangeable?*

**First property examined:** 2D versus 3D? The 3 dimensional solution figure would be too complex. Breakthrough will come from some other property.

**What if a new square inside the squares be formed instead of the conventional adjacent external position?** Yes, that must be the only possibility.

Breakthrough conclusion:A new square can only be created inside squares that are two adjacent ones.

An example of three squares using this innovative idea and 9 matches instead of the usual minimum 10 shown.

The sticks 1 and 3 are placed vertically inside the left and right square ensuring that the distance between them is equal to one stick length.

In our figure, sticks 1 and 3 are placed at midpoints of the top sides of the left and right squares. By this stratagem, the top side of the new square shares in total one stick length from the two squares. Similarly, the bottom side of the new square shares one more side in total between the left and right square bottom sides. Number of sides common becomes thus 3 enabling us to form 3 squares from 12 - 3 = 9 sticks.

This is an innovative technique we name as

Square in Square technique.

It is now easy to form the solution using the square in square technique. Solution figure is shown.

The three sticks 1, 2 and 3 are moved inside the three adjacent horizontal squares and placed vertically at one stick distance separation. By this we have been able to create 5 squares plus one square at the top. A total of six squares.

#### Do you think this is the only solution?

**Consider a variation:** Move the three sticks from the top square instead of the bottom square. Will it be a new solution? It will not be. If you rotate the new figure by 180 degrees it becomes same as the first solution.

In the same way, if the three sticks of the left square or the right square are placed horizontally inside the three vertically adjacent squares, two more solutions may be created.

Again, if you move any of these by 90 degrees it will be same as the first one.

*Rotationally equivalent solution is one.*

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