5/16/2023 0 Comments 1 2 3 4 pen trickIn the remaining two moves this would be impossible to do. If you move any of the four check-marked sticks it will create immediately 4 free-standing sticks to settle later. This four square figure is interesting in the sense that, if you move any of the 12 sticks first, at least 2 common sticks will lose their common property.īut can you move any of the four check-marked common sticks? Think over. This concept plays an important part in solving matchstick puzzles. Two squares will be destroyed and 1 new square will be created by the sticks moved. The important side-effect of these steps is, And then identify two more sticks to eliminate two more common sticks. We are now nearly ready to identify the 1 stick to move that eliminates two common sticks at one go. Now look at the 4 square problem figure below with 4 common sticks check-marked and eight other sticks numbered as 1 to 8 for convenience of explaining the solution. ![]() This is based on mathematical limitation that you cannot split number 4 into three positive integers with the maximum value of 1. You can eliminate 4 common sticks in 3 moves ONLY IF you eliminate at least TWO common sticks in a single move. Without looking at the figure, apply your REASONING to realize that, Your target is to eliminate all four common sticks in 3 stick moves, and you’ll identify the suitable sticks to move by second phase of Structure analysis. First solution by common stick elimination technique: Move 3 matches to make 3 squares matchstick puzzle Second phase of puzzle structure analysis This gives rise to TWO POSSIBLE APPROACHES for solving this puzzle. Note that if you manage to eliminate all four common sticks in three stick moves, the four square figure would automatically be converted to a three independent square figure and vice versa. This is the outcome of the first phase of analysis of the structure using matchstick puzzle domain knowledge of common sticks. In this second step, you have precisely and clearly understood what you have to do to solve the puzzle. What is not mentioned explicitly in these three tasks is-in the process you also reduce number of squares by 1. This is the key pattern identification.Ĥ common sticks reduced the maximum requirement for 4 squares from 16 to 12. You have exactly 12 sticks, the maximum number required to form 3 independent squares. Now look at our 4 square figure again-this time we have labeled the squares by A, B, C, and D, so that we can refer to a specific square. No square in a 16 stick figure of 4 independent squares would have any stick common with any other square. The 4 common sticks in the puzzle figure reduced the requirement of 16 sticks to form 4 independent squares to 16−4=12 sticks. But the fact remains that,Įach common stick between two unit shapes reduces the number of sticks required to form a figure with the two shapes independent from each other- by ONE. In another puzzle, the figure could have equilateral triangles. In our problem, the unit shape is a square. This is where the key concept in matchstick puzzle solving comes in- the concept of sticks common between two adjacent unit shapes. How could then 4 squares have been formed even with the number of sticks 4 less than the number needed to form 4 squares? So to form 4 squares 16 sticks would have been used-4 more than the 12 sticks we have. How many sticks are required to form a SINGLE square? It is 4. Outcome is, clear idea on steps to be taken to reach the solution. In the first step, you need to count the total number of sticks and then in the second step, analyze the difference between given puzzle figure and the goal solution figure. First stage: Structural analysis to know what exactly you have to do We’ll first take up an analytical approach to arrive at conclusions based on matchstick puzzle concepts and deductive reasoning. ![]() Systematic Solution to the matchstick puzzle: Move 3 matches to make 3 squares You should give it a try before going through the detailed solutions. ![]()
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