2017 UNCO Math Contest II Problems/Problem 6
Problem
The Spider's Divider
On a regular pentagon, a spider forms segments that connect one endpoint of each side to n different non-vertex points on the side adjacent to the other endpoint of that side, going around clockwise, as shown. Into how many non-overlapping regions do the segments divide the pentagon? Your answer should be a formula involving n. (In the diagram, n = 3 and the pentagon is divided into 61 regions.)
Solution
We can see that the web is made out of 5 congruent regions surrounding one central region. to find the number of parts in one of the five congruent regions, which is basically sections each divided by lines, so each section is divided into parts. The formula is thus or
See also
2017 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |