Remove 4 sticks to leave 3 triangles in hexagonal wheel puzzle

You are here

Hexagonal wheel to 3 triangles by removing 4 sticks

Remove 4 sticks to leave 3 triangles in hexagonal wheel puzzle

Matchstick puzzle: Remove 4 sticks to leave 3 triangles in hexagonal wheel

Remove 4 sticks to leave 3 triangles in hexagonal wheel matchstick figure. Recommended time to solve 8 minutes.

Hint: First solve: Remove 3 to leave 4.

How many ways can you do it?

Remove 4 sticks to leave 3 triangles in hexagonal wheel puzzle figure

Give it a try. It won't be difficult.

Instead of any random approach we'll solve the puzzle systematically. We'll use common stick analysis on the structure to discover the key information needed to reach the solution.

We'll ask ourselves a series of important questions, analyze the puzzle for answer and make conclusions.

Solution to the matchstick puzzle: Remove 4 sticks to leave 3 triangles in hexagonal wheel: By Common stick analysis and Question analysis answer technique

The first job when solving any matchstick puzzle is to count the total number of matchsticks. It is 12 in six triangles forming the wheel of a hexagon.

Then we ask two questions,

Question 1: How many matchsticks are needed to form 6 independent triangles? It is simply 18.

Question 2: How could then only 12 matchsticks form the six triangles?

Answer 2: As the 6 triangles have between them also 6 common sides of matchsticks, by the concept of common matchstick, each common matchstick would reduce the number of sticks needed to form independent triangles by 1. Six common matchsticks would reduce number of matchsticks needed from 18 to 12.

The common stick concept is explained in the following section in more details. To skip this section click here.


Concept of common stick between two triangles

The following figure shows two independent triangles formed by 6 sticks on the left joined to form a single structure of two triangles separated by one common stick on the right.

The requirement of number of sticks to form the two triangles is reduced from 6 to 5 because of the single common stick between two triangles. Being a common side, it plays the role of two sides of the two triangles. This reduces the actual requirement of number of sides by 1.

Remove 4 sticks to leave 3 triangles in hexagonal wheel puzzle - Common stick between 2 triangles

Thus the requirement of number of sticks to form the two triangles is reduced from 6 to 5 because of 1 common stick.


This makes it clear about what we have in the puzzle figure.

Next question is crucial. It asks about the solution. We have to know about the solution also, isn't it?

Question 3: What would be the total number of sticks and the number of common sticks in the solution figure?

Answer 3:

  1. After removing 4 from 12, there would be 8 matchsticks left. Fine. What about common sticks?
  2. As three independent triangles would need 9 matchsticks, with 8 matchsticks, the solution figure would have to have 1 common stick between two triangles with the third triangle as independent.

Question 4: How would the solution figure look like? We are trying to actually find a solution figure just by analysis and reasoning.

At this point, let us have a look at a figure of three equilateral triangles, but made up of 9 sticks by the very simple action of removing three alternate sticks on the periphery as shown below.

Remove 4 sticks to leave 3 triangles in hexagonal wheel puzzle - 3 independent triangles

Well, reducing need of one more stick is dead easy from this point. Just merge the top two triangles, and you will have your solution figure shown below.

Remove 4 sticks to leave 3 triangles in hexagonal wheel puzzle - Solution figure

Don't stop at this point. we have not solved the puzzle yet, rather we are now quite past the halfway mark. We do not know yet which 4 matchsticks are to be removed to get our solution.

That shouldn't be a problem at all. Just compare the solution on the right and the puzzle figure on the left and you will know.

Remove 4 sticks to leave 3 triangles in hexagonal wheel puzzle - Solution Comparison

Fix top two adjacent triangles of the puzzle figure, A and B, as not to be touched along with a third triangle C not having any common side with either of the two fixed. Leaving these three, simply remove the rest of the matchsticks from the puzzle figure. The number of matchsticks removed would certainly be 4 and you would be left with three triangles. It is logic and an account of common matchsticks.

The solution is shown below.

Remove 4 sticks to leave 3 triangles in hexagonal wheel puzzle - Final Solution

You can solve the puzzle in any way you may feel. Do try. And try to beat this simple path to the solution.

How many solutions would be possible?

That also is easy to see.

The solution figure satisfies the simple but stringent criterion,

Out of the three triangles, two triangles must have one common side but not the third.

As the puzzle figure is rotationally symmetric, whatever way you choose these three triangles, all such choices would be same when rotated.

Rotationally unique solution is only 1.

Happy puzzling.


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

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

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


Share