Puzzle: A matchstick puzzle is given below, move 3 matchsticks to get 3 squares. Give all the possibly unique solutions for the given problem. Solution: Let’s discuss a step-by-step solution to arrive at a result. 1. Count the total number of matchsticks available in the problem. In the figure, the total number of matchsticks is equal to 12 as shown below figure. 2. Now for making a square 4 sticks are used so, to form 4 squares 16 sticks would have been used but we have only 12 sticks. Here the concept of sticks common between two adjacent unit shapes comes. Sticks 5,4,6,10 are common matchsticks 3. Now to make 3 squares 4 * 3 = 12 sticks are required (at max, when sticks are not common between squares). And in this case, 12 matchsticks are available. Now, all we have to do is-
4. Concept of promising stick
Marked sticks are promising sticks Solution 1: Common stick elimination technique Number 4 cannot be split into three positive integers with a minimum value of 1. One of the three numbers has to be 2. By applying Reasoning, 4 common sticks can be eliminated in just 3 moves as- 1. Move stick numbered 2 first. This destroys 1 square and eliminates 2 common match sticks. 2. Move stick numbered 3. This results in two free sticks gained, two common sticks eliminated (like 5, 4 are not common sticks now) and 1 square reduced. 3. Move 3rd stick such that it eliminates 2 more common sticks and destroys 1 more square.
The only feasible solution for this step is to select stick 8. 3 Squares are formed Hence 3 more solutions can be concluded by this method as shown. Solution 2: If sticks 1,7,12 are considered for movement instead of 2,3,8 in the first solution. Solution 3: If sticks 1,7,11 are considered for movement instead of 2,3,8 in the first solution. Solution 4: If sticks 8,9,2 are considered for movement instead of 2,3,8 in the first solution. How many matches are needed to create 4 squares?Conclusion 2: The four squares in solution will be independent squares with no common stick between them. A single common stick would have reduced the number of sticks required to 15. 16 matchsticks would be enough to make these four independent squares.
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