Matchstick puzzles: Move 3 matches to take the cherry out of wine glass and move 2 matches to take the cherry out
Part I: In the figure shown, move 3 matches to take the cherry out of wine glass. The glass shape must not be deformed.
Recommended time limit: 5 minutes.
Part II: In the same figure shown, move 2 matches to take the cherry out of wine glass. The glass shape must not be deformed.
Recommended time limit: 20 minutes.
The matchstick puzzles are the first of its kind. The same starting puzzle figure for the two puzzles doesn't have any closed shape or a structure that is to reformed independently - the matchstick structure is tied down with a second object, a cherry inside it.
Though the wine glass doesn't have any closed shape, it has two areas defined by its shape - area inside the glass and outside it.
The number of matchsticks being very small, only 4 in number, the puzzle should be easy to solve, you feel. So go on, solve the two puzzles. It will surely be fun.
Solution to the first part of the matchstick puzzle: Move 3 matches to take the cherry out of wine glass without deforming the glass
Let's first see what are the components of the wine glass.
The first component that attracts attention is the matchstick forming the BASE. The cherry rests comfortably at the middle of the base BETWEEN the two upright SIDE STICKS. The fourth matchstick at the bottom forms the STEM of the glass.
Necessary conditions for solution
For the cherry to be out of the glass,
- The base stick must be shifted to the right or left away from the cherry, and,
- One of the upright sides must be shifted away so that the cherry no longer rests between them.
Taking a practical approach, first compare the number of sticks in the glass and the number of sticks to be moved. You have four sticks in the glass and three are to be moved. It means, only one stick is not to be moved.
At this point, you can visualize the solution, if you have not done it already.
But we won't deviate from our rigorous analytical reasoning approach.
We will ask the most important question at this point.
Question 1: Which sticks must be moved for the solution?
Answer 1: The matchstick forming the base must be on the right or left of the cherry for the cherry to be outside the glass. So this is the match that must be moved.
Question 2: Is there any other stick that must be moved?
Answer 2: The stem must also be moved to place its head at the middle of the base to become the stem again.
That decides the solution for sure.
One of the upright side sticks will remain in its original position unmoved. Barring this, move the other three sticks and you'll have the solution.
The base stick can slide left or right. Both are equivalent to each other. Let us slide it to the right by one stick length.
That decides the previously right side stick to remain fixed in its position and change its role in the new wine glass as the left upright side stick.
Move the previous stem horizontally right also by one stick length to regain its role as the stem of the new glass.
Lastly, place the previous left side stick as the right side stick of the new wine glass to complete the new wine glass.
The cherry is now on the left of the wine glass and outside it.
The following is the solution figure of the first puzzle. Original Stick positions are shown faded for clear visualization.
Let us take up solving the second puzzle now.
Solution to the matchstick puzzle: Move 2 matches to take the cherry out of the wine glass without deforming the wine glass
The puzzle figure is shown below again,
How to proceed? You may wonder, is it possible at all to take the cherry out of the glass by moving less than 3 sticks?
There seems to be no way it can be done. You face an apparent impossibility. This is why the puzzle is generally classified as a hard puzzle.
But we categorize it further as a lateral thinking class of puzzle.
A lateral thinking puzzle looks simple but no solution can be found easily however hard you think.
There always is a solution to such a puzzle that needs thinking in a radically different way to find it. You would either solve a lateral thinking puzzle quickly or won't be able to solve it at all. These are always fun to solve.
Let's get down to solve this cute little beautiful puzzle.
We will solve it first using our fail-safe Dimension discovery technique.
First solution of matchstick puzzle: Move 2 matches to take the cherry out of the wine glass without deforming the wine glass
Let's reproduce the wine glass with Cherry.
By now we know that it is impossible to take the cherry out of the wine glass by moving 2 sticks by conventional approach unless we discover an altogether ignored dimension or property of the wine glass and use the new information for the solution.
Asking a series of important questions and analyzing for answers, the first question we raise,
Question 1: What are the important dimensions or properties of wine glass as a whole?
Without thinking of its size, you would try to specify something about it as whole that you have taken all along for granted.
The wine glass is normally placed the way it is used. There is nothing more to specify about the wine glass, you decide.
So, you would reason, can we change the normal way of its placement?
"And why not?" will be the clear answer. The glass can very well lie on its sides or even be upside down.
That's it. You have identified the new dimension or property of the wine glass that you have assumed without questioning - its DIRECTION of placement as usual upright.
Answer to question 1: Direction of placement of the wine glass is the dimension or property ignored and assumed unchangeable, though there is no restriction in the puzzle description for changing the direction of placement of the glass.
Question 2: Which direction change would you choose for the solution?
Sideways placement would need too many stick moves, so the only feasible choice is upside down direction.
Answer 2: The wine glass can very well be upside down with previously right side acting as the new stem and the previous stem acting as the right down-pointing side. Slide the base stick a half-stick length right and the previously left side will take up the role of left down-pointing side of the new upside wine glass formation. The cherry will be outside.
The solution figure is shown below.
This is an inventive solution by discovering the lateral thinking possibility using the Dimension discovery technique of finding something about the problem that you have ignored and assumed as unchangeable.
Even though we have suggested an effective and useful method for reaching an inventive solution, still it rests finally on you to discover the NEW DIMENSION that you would change for the inventive solution. You may not be able to discover the new dimension.
There is always a gap to be jumped across to reach an inventive solution.
Such a solution is not fully assured.
With the method of dimension discovery we have tried to shrink the gap to jump across but couldn't eliminate it. There is no method that will hand you over an inventive solution with 100% assurance if you just follow the steps specified in the method.
In spite of this uncertainty though, if you practice and follow a method for finding inventive solutions, in all likelihood you would find it gradually easier to jump across the inventive gap.
We will solve the puzzle now in a more certain and conventional way, using Question, analysis answer technique with fine granularity, going into minute details and leaving nothing uncertain.
Second solution to Matchstick puzzle: Move 2 matches to take the cherry out of wine glass without deforming the glass
Let us show the cherry in the glass again.
This time we will raise question about precisely what you MUST do.
Question 1: Which stick must be moved?
Answer 1: The base stick must be moved. It can be slide right or left. We will slide it right. It will surely remain as the base of the new wine glass.
Now the second question,
Question 2: Which is the second stick that must be moved to form the new wine glass?
Answer 2: The left side stick must be moved, because it is now lying unconnected to any stick of the new wine glass being formed. So it must be moved somewhere right to make it a part of the new wine glass.
Observe: that even though the question 2 was same as that in the solution to the first puzzle, answers are different. In the first case, we have jumped onto a convenient conclusion with so many sticks at our disposal. In this second case, we have to be logically and precisely right.
That leaves the two sticks - the previously stem-stick and the previously right side-stick to be kept untouched in their original position.
Question 3: How can the stem-stick be kept unmoved and still be in the role of the stem of the new glass when the base has already been shifted right?
This is the crucial point where you have to find the answer to the focused question as,
Answer 3: The only way the stem can still be a part of the new wine glass without being moved is, if it acts as one of the two sides of the new wine glass.
Immediate question 4: How can the existing stem act as a side of the new wine glass?
Answer 4 is now easy: Only if the stem acts as the right down-pointing side of an upside down wine glass.
As soon as you find the answer to the last question, all the pieces of the puzzle fall into the right places.
The solution figure is shown again.
Observe that in this second approach also you have reached the inventive solution, but without making any uncertain guess of discovering the ignored dimension or property.
You have evaluated the possibilities efficiently, gradually narrowing down the possibilities to a single one through a series of questions, analysis to find the answer and making conclusions.
This Question, analysis and answer is an immensely powerful method for finding solution to difficult problems. But again, offhand we can say, this method is not maths. It needs cultivating a not so precise and constrained discipline.
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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