Difference between revisions of "2016 UNCO Math Contest II Answer Key"
(Replaced content with " 1) <math>84</math> 2) <math>2^6 \cdot 3^2 \cdot 7^3\cdot 11^2 \cdot 13\cdot 17\cdot 19\cdot 23</math> 3) <math>\frac{2\sqrt{3}}{1+2\sqrt{3}}=\frac{12-2\sqrt{3}}{11}</...") (Tag: Replaced) |
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1) <math>84</math> | 1) <math>84</math> | ||
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5) <math>0.332</math> | 5) <math>0.332</math> | ||
| − | 6) (a) <math>\frac{3}{4}</math> | + | 6) (a) <math>\frac{3}{4}</math> (b)<math>\frac{15-\sqrt{65}}{8}</math> |
| − | (b)<math>\frac{15-\sqrt{65}}{8}</math> | ||
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7) <math>\frac{5}{4}</math> | 7) <math>\frac{5}{4}</math> | ||
| − | + | 8) a)<math>994</math> b) <math>\frac{1}{120}n(n + 1)(n + 2)(8n^22 + 11n + 1)</math> | |
| − | 8) a)<math>994</math> | ||
| − | b) <math>\frac{1}{120}n(n + 1)(n + 2)(8n^22 + 11n + 1)</math> | ||
9) There are <math>\frac{64!}{56!4!4!}</math> arrangements of the colored pawns on the standard board. | 9) There are <math>\frac{64!}{56!4!4!}</math> arrangements of the colored pawns on the standard board. | ||
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10) There are <math>\frac{1}{32}[\frac{64!}{56!4!4!} + 3\frac{ 32!}{28!2!2!}+ 12\frac{16!}{14!1!1!}]= 9682216530 </math> different wallpaper patterns. | 10) There are <math>\frac{1}{32}[\frac{64!}{56!4!4!} + 3\frac{ 32!}{28!2!2!}+ 12\frac{16!}{14!1!1!}]= 9682216530 </math> different wallpaper patterns. | ||
Latest revision as of 03:00, 13 January 2019
1) 
2) 
3) 
4) There are eighteen such numbers:
5) 
6) (a) 
(b)
7) 
8) a)
b) 
9) There are 
arrangements of the colored pawns on the standard board.
10) There are ![$\frac{1}{32}[\frac{64!}{56!4!4!} + 3\frac{ 32!}{28!2!2!}+ 12\frac{16!}{14!1!1!}]= 9682216530$](http://latex.artofproblemsolving.com/3/3/f/33fd69678909703cb7f56b1be4c59c9bb85f3c6b.png)
different wallpaper patterns.
