How many matchsticks will there be in Step 33, Step 84, and Step 108? Of course, we can draw and count. Class 7

How many matchsticks will there be in Step 33, Step 84, and Step 108? Of course, we can draw and count. Class 7

Question 1.

How many matchsticks will there be in Step 33, Step 84, and Step 108? Of course, we can draw and count, but is there a quicker way to find the answers using the pattern present here? Class 7

Solution:

Number of matchsticks needed at Step 33

= 3 + 2 (33 - 1) = 3 + 2 × 32 = 3 + 64 = 67.

Number of matchsticks needed at Step 84

= 3 + 2 × 83 = 3 + 166 = 169.

Number of matchsticks needed at Step 108

= 3 + 2 × 107 = 3 + 214 = 217.

Question 2.

Does the above expression also give the number of matchsticks at each step correctly? Are these expressions the same? Class 7

Solution:

Yes, yes.

Question 3.

What are these numbers in Step 3 and Step 4? Class 7

Solution:

In Step 3 :

Horizontally: 3

Diagonally: 4

In Step 4 :

Horizontally: 5

Diagonally: 6

Question 4.

How does the number of matchsticks change in each orientation as the steps increase? Write an expression for the number of matchsticks at Step ‘y' in each orientation. Do the two expressions add up to 2y + 1? Class 7

Solution:

Number of matchsticks increases by 2 in each step horizontally as well as diagonally.

In Step 4 : Horizontally : y

Diagonally : y + 1

Total : 2y + 1

Yes.