You are here

First Move 3 sticks and make 2 squares matchstick puzzle

Move 3 matches to make 2 squares matchstick puzzle 1

Move 3 matches to make 2 squares matchstick puzzle 1

In puzzle figure, move 3 matches to make 2 squares.

How many unique solutions can you find?

Time limit: 5 minutes.

Unique solution: If you rotate the solution figure in any way, it will still remain unique.

Give it a try. It will be fun.

Comment

The puzzle is different from the matchstick puzzles we see usually. There is no complete square or triangle in the puzzle figure.

It looks as if the figure is incomplete.

1st move 3 matches to make 2 squares matchstick puzzle

How to solve it?

You may select any 3 sticks you like and try to place the sticks to make 2 squares. That would be the trial and error method. Usually that takes more time.

Instead, spend a little time to analyze the puzzle figure. Think about how the solution figure would look like. And then decide on your stick moves. You would solve the puzzle quick this way.

Solution to Move 3 matches to make 2 squares matchstick puzzle 1: By Structural analysis Identify which sticks to move and where to move

First stage: Analysis of number of sticks used and conclusions

Take the first step. Count the number of sticks. It is 10.

Make the first conclusion.

Conclusion 1: To make 2 squares by these 10 sticks, the 2 squares must be of UNEQUAL SIZE.

Reason for unequal size: To make two squares MAXIMUM number of sticks required is 8 when the two squares do not have any common side. Puzzle figure has 10 sticks, more than the maximum.

That's fine. Easily accepted.

Question: But what would be the size of the two unequal squares in the solution figure?

With a little thought, make the second conclusion,

Conclusion 2: The two squares must be: One large square of 2 stick sides and one small square of 1 stick sides.

Reason:

A large square with 3 stick sides requires 12 sticks for its 4 sides. This is more than number sticks in puzzle figure.

As two squares with 2 stick sides is not possible, one large square MUST BE of 2 STICK SIDES and one small square of 1 stick sides.

Okay. But how would the two squares be placed in the solution figure?

Analyze the number of sticks available and number of sticks required to make two such squares.

Also use the concept of COMMON STICK. Each common stick between two squares reduces number of sticks required to make the squares by 1.

Conclusion is easy.

Conclusion 3: One square of 2 stick sides requires 8 sticks. 2 more sticks are left from 10 available. A single small square requires 4 sticks making total sticks required 12. So 2 sticks must be common between the two squares.

Question: What can be the location of the small square with respect to the large square?

Conclusion 4: The small square cannot be located outside the large square as it would have then only 1 stick common with the large square. Need is for 2 common sticks. isn't it?

Conclusion 5: That means—the 3 STICKS TO MOVE must be the three sticks of the small square in the puzzle figure leaving its right vertical stick.

This settles first issue—which sticks to move.

The following figure shows the results of reasoning achieved till now. You are now sure that the check-marked sticks are the sticks you have to move.

1st move 3 matches to make 2 squares matchstick puzzle - sticks to move

Nothing random or extraordinary you have done. It has all been common sense reasonable questions and clear conclusions.

Final stage of Solution to Move 3 matches to make 2 squares matchstick puzzle 1: Where to place the 3 sticks?

The large incomplete square has two gaps to close on its right side. Isn't it?

So move two of the check-marked sticks to close the two gaps. The large square is now complete and one stick left to move.

Look at the figure you have made by the two stick moves. What do you see?

Conclusion 6: Using the stick left, a small square can be completed in TWO WAYS. At top right or bottom right.

Both are solutions to the puzzle.

Following figure shows the solutions.

1st move 3 matches to make 2 squares matchstick puzzle solutions

So you have found not one, but two solutions to the puzzle step by step.

But the question is—are these two solutions rotationally unique?

Second part of solution to Move 3 matches to make 2 squares matchstick puzzle 1: How many rotationally unique solutions?

Just rotate the first solution figure by 90 degrees clockwise and you will get the second solution. These two are equivalent.

Rotationally UNIQUE SOLUTION IS ONLY 1.

You may find it fun to solve also the second move 3 matches to make 2 square matchstick puzzle. Only difference in these two cute puzzles is in their puzzle figures.

Takeaway

The puzzle is easy to solve. But it feels good to know exactly what to do and why to do it. All through the steps of solving the puzzle. Isn't it?

This is systematic problem solving by analytical reasoning step by step.

Concepts used: Common sense reasoning and matchstick structure concept of common sticks.

End Note

If you form your own matchstick puzzle and solve it exhaustively using all methods you know and can create, it will be a richly rewarding experience as well as interesting pastime.


Puzzles you may enjoy

Riddles

Two jugs riddle

The tramcar reunion riddle

Riddle of 4 persons crossing a bridge over a river at night

Three boxes riddle

Riddle of PROBLEMSOLVING - Creation and application of Repetition pattern based technique

Airplane riddle of flying around the world

Riddle of lying and truth-telling twins

Two jugs riddle of delivering 1 quart of milk each

How could Sonia sell half a poodle riddle

Transfer a pile of 15 numbered discs riddle

Mathematical puzzles

Reverse cheque puzzle

Reverse cheque puzzle solution

Counting eggs puzzles based on Euclid's division lemma

Monkey and the coconuts puzzle with solutions

10 digit Conway number puzzle with solution

World's Hardest Easy Geometry Puzzle Solved with Techniques Explained Step by Step

Hard Algebra Puzzles Solved by Basic Exponent Concepts and Reasoning

Three squares in a triangle puzzle

9 squares in a rectangle math puzzle

How many addition signs needed to make sum of 99

Logic analysis puzzles

Method based solution to Einstein's logic analysis puzzle, whose fish

How to solve Einstein's puzzle whose fish confidently, improved method based solution

Logic puzzle, When is Cheryl's birthday

Liar and truth-teller riddle with step by step easy solution

4 Prisoners and Hats Puzzle

Liar, Truth-teller, Random-answerer riddle

River crossing puzzles

Farmer with fox, goose and bag of corn crossing the river puzzle

Two pigs and two hens crossing river puzzle

3 monkeys and 3 humans crossing river puzzle

King queen minister washerman river crossing puzzle

Ball weighing puzzles

Find the heavier among 8 identical balls in 2 weighing puzzle

Find the fake ball among 8 identical balls in 3 weighing puzzle

Find the fake ball among 9 identical balls in 3 weighing puzzle

Find the fake ball among 12 identical balls in 3 weighing hard puzzle with solution

Matchstick puzzles

Solution to 6 triangles to 5 triangles in 2 moves, first matchstick puzzle

Matchstick puzzle 5 squares to 4 squares in 2 moves

Matchstick puzzle 5 squares to 4 squares in 3 moves

Matchstick puzzle, Turn around the fish in 3 moves

Fifth Matchstick puzzle, Move 3 sticks in tic-tac-toe figure to form 3 perfect squares

Hexagonal wheel to 3 triangles by removing 4 sticks

Convert 5 squares to 4 squares in 3 stick moves, third 5 square matchstick puzzle

Matchstick Puzzle - Make the kite nose-dive in 5 stick moves

Make 5 squares from 6 in 2 stick moves - 6 square matchstick puzzle

Move 3 sticks and convert 5 squares to 4 squares in 4th 5 square matchstick puzzle

Move 3 sticks and convert 4 squares to 3 squares matchstick puzzle

Move 8 sticks and convert 5 squares to 2 squares matchstick puzzle

First Move 3 sticks and make 2 squares matchstick puzzle

Second Move 3 sticks and make 2 squares matchstick puzzle

Remove 3 matchsticks to leave 6 triangles puzzle

Add 3 matchsticks to make 4 triangles - lateral thinking stick puzzle

Move 1 stick to make 4 closed shapes each with 3 or 4 sides

Move 2 sticks to make 5 closed shapes matchstick puzzle

Move 2 to make 7 squares matchstick puzzle - solution based on problem solving and innovation model

Move 4 to turn the tower upside down Matchstick puzzle

Move 2 matches to make 6 squares and move 8 matches to make 6 squares - a pair of matchstick puzzles

Move 3 matches to take the cherry out of wine glass and move 2 matches to take the cherry out - a pair of matchstick puzzles

Move 6 matches to make 5 squares

Move 2 matches and add 1 to make 2 diamonds puzzle

Move 4 matches to make 5 triangles matchstick puzzle

Remove 4 matches to leave 4 equal triangles puzzle

Transfer 1 match in two matchstick groups puzzle

Move 3 matches to make 5 equal squares puzzle