2016 UNCO Math Contest II Answer Key

1) $84$

2) $2^6 \cdot 3^2 \cdot 7^3\cdot 11^2 \cdot 13\cdot 17\cdot 19\cdot 23$

3) $\frac{2\sqrt{3}}{1+2\sqrt{3}}=\frac{12-2\sqrt{3}}{11}$

4) There are eighteen such numbers: $4, 9, 10, 14, 15, 21, 27, 35, 44, 50, 52, 68, 75, 76, 81, 92, 98, 99$

5) $0.332$

6) (a) $\frac{3}{4}$ (b) $\frac{15-\sqrt{65}}{8}$

7) $\frac{5}{4}$

8) a) $994$ b) $\frac{1}{120}n(n + 1)(n + 2)(8n^22 + 11n + 1)$

9) There are $\frac{64!}{56!4!4!}$ arrangements of the colored pawns on the standard board.

10) There are $\frac{1}{32}[\frac{64!}{56!4!4!} + 3\frac{ 32!}{28!2!2!}+ 12\frac{16!}{14!1!1!}]= 9682216530$ different wallpaper patterns.

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