Count the semicircles again

Probability Level 2

Figure 1:-

Figure 2:-

Figure 3:-

Calculate the number of semicircles in the ${2016}^\text{th}$ figure.

1 solution

Ashish Menon
Apr 17, 2016

In 1st figure there are $4$ semicircles.
In 2nd figure there are $7$ semicircles.
In 3rd figure there are $10$ semicircles.

So, we see that in nth figure, there are $3n + 1$ semicircles. So, in 2016th figure, there would be $(3 × 2016) + 1 = \boxed {6049}$ semicircles.

There is a mistake in the third line, it should be 10 semicircles.

Sravanth C. - 5 years, 1 month ago

Thanks, I did it

Ashish Menon - 5 years, 1 month ago