Question

Look at the following matchstick pattern of squares (fig 11.6). The squares are not seperate . Two neighbouring squares have a common matchstick. Observethe patterns and find the rule that gives the number of matchsticks in terms of the numbers ofthe squares.( Hint : If you remove the vertical stick atthe end you will get a pattern of Cs.)

Answer 1

Number of match sticks in figure(a) = 4 = 3 × 1 + 1

Number of match sticks in figure (b) 7 = 3 × 2 + 1

Number of match sticks in figure (c) = 10 = 3 × 3 + 1

Number of match sticks in figure (d) = 13 = 3 × 4 + 1

Here, the number of match sticks is 1 more than thrice the number of square in the pattern.

So, the rule that gives the number of match sticks in terms of number of square is 3 × n + 1 = 3n + 1, where n is the number of squares.