Add 10 matches to 4 matches of a diamond to create 5 diamonds puzzle
To the puzzle figure of a single diamond, add 10 matches to create 5 diamonds. No matchstick should be left alone hanging.
The Puzzle
In the following figure of a single diamond made up of four sticks, add 10 matches to create 5 diamonds.
Recommended time to solve 15 minutes.
Try to solve before going through the solution.
After the solution we will solve a second variation of the puzzle.
Solution to the matchstick puzzle add 10 matches to create 5 diamonds: Common stick analysis
When you add 10 sticks to the existing 4, you will have 14 sticks and 5 diamonds. As each diamond takes 4 sticks, you need 20 sticks to make 5 independent diamonds. When you make 5 diamonds with 14 sticks then, you must have 20-14=6 common sticks in the figure.
6 common sticks in 5 diamond figure is a large number. You have to take every opportunity to increase the number of common sticks. In other words, the final figure must be very compact.
Without worrying about the final figure, you take an incremental approach of adding three sticks to make 2 diamonds as shown.
You have added the sticks 1, 2 and 3 to create the second diamond with an addition of one common stick.
It is just a step more in the same incremental direction to get the most compact four diamond figure.
In all probability, this structure should be a part of the solution. Question is—how can you add just 2 sticks to add one more diamond?
You cannot add two sticks on the outside of the four diamond figure to create a new fifth diamond. What is the way out?
It is not just adding the fifth diamond, you have to add also two common sticks by adding the two sticks.
That means,
Conclusion 1: You have to add the two sticks to the most compact four diamond figure in such a way that each stick becomes a common stick.
Here, you remember the special property of a diamond,
Special property of a diamond: If you place a stick along the shorter diagonal of the diamond you create two matchstick triangles of equal sides.
You use this concept to create the unusual solution easily.
The two sticks are placed as diagonals of two diamonds one below the other, so that a vertically oriented fifth diamond is created along with two new common sticks.
Second add 10 matches to create 5 diamonds matchstick puzzle
In the following puzzle figure of a single diamond, add 10 matches to create 5 diamonds without any triangle.
Recommended time to solve is 20 minutes.
This is a harder puzzle, but give it a good try before going through the solution.
Solution to the second add 10 sticks to create 5 diamonds matchstick puzzle: Identifying must-have components in the solution
As triangles are prohibited,
First conclusion: The solution must comprise only diamonds.
It means,
You have to form 5 diamonds with 6 common sticks using 14 matchsticks.
Thinking incrementally again, you decide you must have the two figures of two diamonds as shown.
As an intermediate step, there is no other way than to form such a pair of two diamond figure each with one common stick. Together, the four diamonds have 2 common sticks and four diamonds with 14 sticks used up.
To free two sticks, you have earlier merged sticks 1 with 2 and sticks 3 with 4 to create the most compact four diamonds with 12 sticks and four common sticks. But now you cannot do that as you cannot reach the solution this way by adding diagonal sticks and creating triangles.
Second conclusion: Though it seems impossible, you have to somehow join these two figures of two diamonds without merging sides to create the fifth diamond with four common sticks.
This gives you a new promising idea. The second conclusion implies,
Third conclusion: You cannot merge any of the sides of the two figures.
And also,
Fourth conclusion: All four sides of the fifth diamond created by joining the two figures must be common sides.
That means,
Fifth conclusion: You can join only two pairs of nodes of the two figures to create the fifth diamond.
With so much knowledge, the solution becomes clear to you. But you take proper care to form the solution accurately, as shown.
The two diamond figures are joined together at nodes A and B so that a new diamond is created by the sides 1, 2, 3 and 4 each of which acts as a common side between two diamonds.
To show that the diamond is created perfectly, a faded out stick is placed as a faded out diagonal.
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