Art of Problem Solving

AoPS Online

2014 UNCO Math Contest II Answer Key

Revision as of 03:54, 22 October 2014 by Timneh (talk | contribs) (Created page with "1) The youngest will be <math>16</math> and the perfect square is <math>100</math>. 2) <math>145</math> 3) <math>x =-2</math> and <math>y = \tfrac{-3}{4}</math> 4) (a) <mat...")

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

1) The youngest will be $16$ and the perfect square is $100$ .

2) $145$

3) $x =-2$ and $y = \tfrac{-3}{4}$

4) (a) $210$ (b) $4010$ (c) $\tfrac{n(n^2+1)}{2}$

5) (a) $\tfrac{1}{5}$ (b) $\tfrac{(1-x)^2}{1+x^2}$

6) (a) $11$ (b) $76$

7) $\ftrac{112}{125}$ (Error compiling LaTeX. Unknown error_msg)

8) (a) $\tfrac{2}{5}$ (b) $\tfrac{8}{31}$

9) Zero probability for $n=1$ and $\frac{F_{n-1}}{2^{2n}}$ for $n\ge 2$ , where $F_{n-1}$ is the $(n-1)^{st}$ Fibonacci number.

10)(a) $\tfrac{1}{11}$ (b) $\tfrac{2}{11}$ (c) $\tfrac{1023}{5120} = \left(\tfrac{1}{m+1}\right) \tfrac{2^{m+1}-1}{2^m}$ ,

where there are $m$ guessers, not including Tweedledee and Tweedledum. Here $m = 9$ .

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2014_UNCO_Math_Contest_II_Answer_Key&oldid=65403"

© 2024 AoPS Incorporated