Matchsticks are used to build a row of squares that share sides. One square needs 4 matchsticks, two squares in a row need 7, and three squares in a row need 10. How many matchsticks are needed for a row of 10 squares?

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Accepted Answer

31. After the first square, each extra square needs only 3 more matchsticks because it shares one side with the square before it. So for n squares the count is 4 + 3 × (n − 1), which is the same as 3n + 1. For 10 squares this gives 3 × 10 + 1 = 31 matchsticks.

Matchsticks are used to build a row of squares that share sides. One square needs 4 matchsticks, two squares in a row need 7, and three squares in a row need 10. How many matchsticks are needed for a row of 10 squares?

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