Brain Teasers
Segments in a Circle
3 lines can divide a circle into a maximum of 7 regions. What is the greatest number of regions that 100 lines can divide a circle into?
Hint
Try to notice a pattern:If there are 4 lines, there can be at most 11 regions.
If there are 5 lines, there can be at most 16 regions.
If there are 6 lines, there can be at most 22 regions.
Answer
5051.Notice that 100+99+98...+3+2+1=5050, one less from 5051, and 3+2+1=6, one less from the maximum number of regions when there are 3 lines.
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