2006 UNCO Math Contest II Problems
UNIVERSITY OF NORTHERN COLORADO MATHEMATICS CONTEST FINAL ROUND January 28,2006.
For Colorado Students Grades 7-12.
Contents
Problem 1
If a dart is thrown at the 
target, what is the probability that it will hit the shaded area?
![[asy] filldraw((2,2)--(4,6)--(6,6)--(6,4)--cycle,blue); filldraw((2,2)--(6,2)--(6,1)--cycle,blue); filldraw((2,2)--(0,0)--(0,1)--cycle,blue); filldraw((2,2)--(0,4)--(0,6)--cycle,blue); for(int i=0;i<7;++i){ draw((0,i)--(6,i),black); draw((i,0)--(i,6),black); } dot((2,2));dot((0,4));dot((0,6));dot((4,6));dot((6,6)); dot((6,4));dot((6,2));dot((6,1));dot((0,0));dot((0,1)); [/asy]](http://latex.artofproblemsolving.com/d/f/1/df1c252b085c82d7d67511a0e58cc24d9595ae8a.png)
Problem 2
If 
and 
are positive integers, how many integers are strictly between the product 
and 
? For example, there are 35 integers strictly between 
and 
Problem 3
The first 14 integers are written in order around a circle.
Starting with 1, every fifth integer is underlined. (That is 
).
What is the 
number underlined?
![[asy] draw(unitcircle,black); pair A; for(int j=1;j<15;++j){ A=dir(90-(j-1)*(360/14)); MP(string(j),A,A); } [/asy]](http://latex.artofproblemsolving.com/9/5/3/953b3ed19882010780e63c1f5a6644729f8a74d3.png)
Problem 4
Determine all positive integers 
such that 
divides evenly (without remainder) into 
?
Problem 5
Problem 6
==Problem 7
Problem 8
Problem 9
Problem 10
