Sample Problems
Here are a few classic problems from the AIME to give you a taste of what you'll find inside Math Ascent.
The "Escalator Puzzle" (1987 AIME, #12)
Al and Bob are walking on an escalator moving in opposite directions. Al walks down an up-moving escalator and counts 150 steps; Bob walks up the same escalator and counts 75 steps. Al is three times faster than Bob. How many steps are visible?
The "Additional Page" Problem (1986 AIME, #5)
A book has pages numbered $1$ through $n$. Someone adds all the page numbers but accidentally adds one page twice, getting a sum of 1986. Which page was added twice?
The "Three Circles" Problem (1995 AIME, #11)
Two circles of radius 3 and 6 are externally tangent to each other and internally tangent to a circle of radius 9. Find the square of the length of a chord of the large circle that is a common external tangent to the two smaller ones.
The "Log Lunacy" (1995 AIME, #15)
The product of the roots of the equation $(\log_2 x)^4 - 12(\log_2 x)^2 + 4\log_2(x^2) + 23 = 0$ can be written as $1/k$. Find $k$.