## Matchstick area dividing puzzle

4 matches divide the whole into two equal areas of same shape. Move these 4 matches to divide the whole into two equal areas of same shape again.

**Recommended time to solve** is 20 minutes.

Have a go at the puzzle before you refer the solution.

### Solution to the add 4 matches to divide the whole into two equal areas puzzle: Area assessment and shape analysis

With vertical and horizontal matchsticks forming the boundary of the areas, we can easily express the **areas in terms of 1-stick side squares.**

Each of the two equal areas A and B equals six squares and the whole 12 squares.

Conclusion 1:Each of the two areas in the solution will also then equal six squares.

We will do now a brief **shape analysis** of the whole area and the segments as well.

Each of the segments comprise a square formation of 4 square area plus an extension of two square area at one end.

It is highly probable in the new solution that each of the segments will also have the square shape of four square area with two numbers of extensions of 1 square area at two ends. This will make the solution segments different from the puzzle segments. These are conjectures, but highly probable conjectures.

We decide to create two such segments. And with little difficulty, we could form the segments as shown.

Both Area A and Area B are of equal size of six 1-stick side squares. Each of the two segments also have one square shaped four 1-stick square formation with two 1-stick square extensions at two ends. The same matchsticks 1, 2, 3 and 4 are added to get this result.

**Question is:** Are these two areas have **exactly same shape?**

### Solution to the add 4 matches to divide the whole into two equal areas puzzle: Shape equivalence

To have total confidence in the solution, the Area A is separated out from Area B and flipped vertically. Area B is placed beside this flipped Area A. Result shown.

In Area A, the stick 4 that was at the bottom has become the top stick because of the vertical flipping. Now we are totally sure of exactly the same shape of the two areas.

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