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Move 4 matches to form 3 square area

Move 4 matches to form 3 square area matchstick puzzle

In the 4 square area puzzle figure, move 4 matches to form 3 square area. There must be a single area enclosed by matchsticks. Solve on 20 minutes.

The matchstick puzzle

The following matchstick configuration area equals4 squares. The V-shaped formation at the top reduces the top 1 square area to area A equal to one-half square. This reduction is compensated by the outward V-shaped extension of area exactly equal to one-half square at the bottom.

Move 4 matches to form 3 square area puzzle figure

Move 4 matchsticks in the configuration to form an area equal to 3 squares.

Condition: The area must by enclosed by a single matchstick boundary.

Time to solve: 20 minutes.

This puzzle structure has an unusual formation and needs careful structural analysis for solving the puzzle quickly.

Do try before going through the solution.

Solution to move 4 matchesa to form 3 square area: Analysis of structure and sticks to move

The puzzle figure is shown again for convenience.

Move 4 matches to form 3 square area matchstick puzzle graphic

The V formation at the top equals the absence of an area equal to one-half of a square. The V-shaped extension at the bottom is also of area one-half of a square. This compensates the reduction of area at the top so that the total area of the configuration equals 4 squares.

Because of this mutual compensatory relationship, the two V-shapes are strongly coupled with each other in the configuration. If you want to disturb any match in one V, you must analyze its consequence in the other V as well.

Because of this structural coupling of effectively 4 sticks at the top and two sticks at the bottom, you cannot move any of the sticks for solving the puzzle.

Conclusion 1: Reduction of 1 square area must be achieved by moving matchsticks from the left and/or right sides of the puzzle configuration.

Naturally the question arises, how can we collapse the matches on the two sides to reduce area by 1 square?

When you try to achieve this mentally you realize that, solution must come by moving sticks from both sides, not just from one side.

Naturally we wonder whether the V shaped area reduction at the top can be used. It should have a great potential.

Working on this line, we first make a simple trial by reversing the extended V at the bottom. Figure below.

Move 4 matches to form 3 square area matchstick puzzle trial

The inverted V-shaped formation at the bottom inside the middle square reduces its area by one-half square and along with the reduction at the top it effectively forms a 3 square area. But this cannot be the solution because we have achieved this configuration by moving just 2 sticks.

Now we know clearly that on any one side of the configuration we have to form such an inclined V inwards to reduce the area by one-half square.

Following figure shows such a possibility indicated by two inclined dotted lines inwards on the left of the configuration.

Move 4 matches to form 3 square area matchstick puzzle area reduction by one-half square

It is clear that to form this inclined V inwards we need to move 2 matchsticks taking a loan of one free matchstick from the right side.

Stick move scheme for solution: To make a move of total 4 matchsticks then we have to move the single left side vertical matchstick and three matchsticks from the right side. The three sticks convenient to move are the three outer sticks of the right side square.

Following shows the stick move scheme by red marking the sticks to move.

Move 4 matches to form 3 square area matchstick puzzle sticks to move

We have already decided to form an inward inclined V on the left side. What structure should we form on the right?

Answer is clear,

New structure scheme for solution: An inclined V inwards on the left reduces area by one-half square. The three matchsticks identified for moving has also reduced the area by 1 square more. Total reduction till now is 1 and one-half square area. Just increase the area by a new externally extended inclined V with two of the three free sticks on the right side.

The final solution figure shown below,

Move 4 matches to form 3 square area matchstick puzzle solution

The sticks moved are shown also in their original positions faded out. And the stick movements are identified by arrows.

Whole area equals exactly 3 squares and it is enclosed by a single matchstick boundary.

End note

Because of the structural emphasis, solution of this puzzle could be reached not by common concepts of matchstick puzzles such as common stick analysis. Solution depended heavily on structural reasoning. It is still reasoning, but reasoning on the configuration structure.


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