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Algebra

    Matchstick Patterns

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6th class > Algebra > Matchstick Patterns

Matchstick Patterns

Ameena and Sarita are making patterns with matchsticks. They decide to use that knowledge of line segments to make patterns of different alphabets with wooden sticks or simply, a bunch of matchsticks. Ameena takes two matchsticks and forms the letter L. How many matchsticks does she need? .

Then Sarita also picks some sticks, forms another letter L and puts it next to the one made by Ameena Now let us form a pattern of 2 Ls. How many matchsticks do we need? .

Then Ameena adds one more L to the pattern. How many matchsticks are required now? .

Their friend Appu comes in. He looks at the pattern. Appu always asks questions. He asks the girls, “How many matchsticks will be required to make seven Ls”? Ameena and Sarita are systematic. They go on forming the patterns with 1L, 2Ls, 3Ls, and so on. They make a table of the number of Ls formed and the number of matchsticks required to make them.

Number of Ls formedNumber of matchsticks used
12
24
36
4
5
6
7
8
... ...

Appu gets the answer to his question from the above; 7Ls require matchsticks.

While writing the table, Ameena realises that

Number of matchsticks required = × number of Ls.

This is where variables come in. For convenience and generalizing the problem, we can write the letter n for the number of Ls. Now, if we need to find out the number of matchsticks required for making any random number of Ls we can say:

Number of matchsticks required = 2 × 'n''.

If one L is needed, n = 1; If two Ls are needed, n = 2 and so on. Therefore, n can be any natural number 1, 2, 3, 4, 5, ....

Instead of writing 2 × n, we write 2n. Note that 2n is same as 2 × n.

Upon putting the required value in place of n, we get:

For n = 1, the number of matchsticks required = 2 × 1 = 2

For n = 2, the number of matchsticks required = 2 × 2 = 4

For n = 3, the number of matchsticks required = 2 × 3 = 6 etc.

We observe that these results agree with those given in the above table.

Now, tell what are the number of matchsticks required to make 15 Ls?