2010 UNCO Math Contest II Answer Key

1) $153$

2) $210$

3) $12$

4) $(n+1)^2(n^2+1)$

5) (a) $\tfrac{6}{455}$ (b) $\frac{n!}{\binom{n^2}{n}}$

6) $8571$

7) $29$

8) $\frac{3^{2048}-1}{2}$

9) (a) $A=2^8,B=2^6,C=2^5$ (b) $A=3^{20},B=3^{15},C=3^{12},D=61$

10) $\frac{n+2}{2}$ if $n$ is even; $\frac{n+1}{2}$ if $n$ is odd.

11) (a) $6$ (b) $20$ (c) $50$ (d) $1\cdot n^2 + 2\cdot (n-1)^2+3\cdot (n-2)^2 + \cdots + n\cdot 1^2$

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