Difference between revisions of "1971 AHSME Problems/Problem 17"
Coolmath34 (talk | contribs) (Created page with "== Problem == A circular disk is divided by <math>2n</math> equally spaced radii(<math>n>0</math>) and one secant line. The maximum number of non-overlapping areas into whi...") |
m (see also, boxed answer) |
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It seems that for <math>2n</math> radii, there are <math>3n+1</math> distinct areas. The secant line must pass through <math>n</math> radii for this to occur. | It seems that for <math>2n</math> radii, there are <math>3n+1</math> distinct areas. The secant line must pass through <math>n</math> radii for this to occur. | ||
− | The answer is <math>\textbf{(E)} | + | The answer is <math>\boxed{\textbf{(E) } 3n+1}.</math> |
-edited by coolmath34 | -edited by coolmath34 | ||
+ | |||
+ | == See Also == | ||
+ | {{AHSME 35p box|year=1971|num-b=16|num-a=18}} | ||
+ | {{MAA Notice}} |
Revision as of 09:04, 5 August 2024
Problem
A circular disk is divided by equally spaced radii(
) and one secant line. The maximum number of non-overlapping
areas into which the disk can be divided is
Solution
We can draw the cases for small values of
It seems that for
radii, there are
distinct areas. The secant line must pass through
radii for this to occur.
The answer is
-edited by coolmath34
See Also
1971 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.