Difference between revisions of "2011 UNCO Math Contest II Problems/Problem 9"
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== Solution == | == Solution == | ||
+ | (a) <math>T(n+1)+T(n)=\binom{n}{3}</math> | ||
+ | (b) <math>T(N) = \binom{N-1}{3}-\binom{N-2}{3}+\binom{N-3}{3}-\binom{N-4}{3}+\cdots</math> | ||
== See Also == | == See Also == |
Latest revision as of 03:23, 13 January 2019
Problem
Let be the number of ways of selecting three distinct numbers from so that they are the lengths of the sides of a triangle. As an example, ; the only possibilities are , and .
(a) Determine a recursion for T(n).
(b) Determine a closed formula for T(n).
Solution
(a)
(b)
See Also
2011 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |