Puzzle | Maximum pieces that can be cut from a Circle using 6 straight lines

PUZZLE:

Given a Circle and Six Straight Lines. What is the maximum number of pieces that one can cut the circle using these six straight lines?

SOLUTION:

Using six lines, we can cut the circle into 22 pieces at maximum.

• Using one line, the circle can be divided into two parts.

• Two lines divide the circle into four parts.

• Three lines divide the circle into seven unequal parts.

• Four lines cut the circle into eleven parts.

• Using five lines, circle can be divided into sixteen parts.

• Finally, using six lines the maximum parts that can be formed are 22.

We can find out the number of pieces using a mathematical formula also:

Number if pieces  = 1 + (n*(n+1)/2)