2008 Mock ARML 1 Problems
Compute all real values of such that .
A positive integer is a yo-yo if the absolute value of the difference between any two consecutive digits of is at least . Compute the number of -digit yo-yos.
In regular hexagon with side length , intersects at , and intersects at . Compute the length of .
There are black balls and white ball in a hat. A turn consists of picking a ball from the hat and replacing it with one of the opposite color. Compute the probability that, after a sequence of turns, there are black balls in the hat before there are white balls.
The positive real numbers are in arithmetic progression in that order. They also satisfy
Compute the common difference of this arithmetic progression.
Square has side length . is the midpoint of , and is the midpoint of . is on such that is between and , and . Compute the length of .
Compute the number of -digit base- positive integer multiples of that are also divisible by when read in base instead of base .
For positive real numbers ,