Difference between revisions of "2011 UNCO Math Contest II Problems/Problem 9"
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(b) <math>T(N) = \binom{N-1}{3}-\binom{N-2}{3}+\binom{N-3}{3}-\binom{N-4}{3}+\cdots</math> | (b) <math>T(N) = \binom{N-1}{3}-\binom{N-2}{3}+\binom{N-3}{3}-\binom{N-4}{3}+\cdots</math> | ||
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| + | I found (a) <math>T(n) = T(n - 1) + 2(n-4)</math> and (b) <math>T(n) = 13 + n (n - 7).</math> | ||
== See Also == | == See Also == | ||
Revision as of 21:57, 6 November 2022
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) 
I found (a) 
and (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 | ||
