Back to all chapters

AMC Strategies

These strategies can save the day.

A preview of "AMC Strategies" Join Brilliant Premium

What is the sum of all \(x\cdot y\) where \((x,y)\) is an integer solution to \[xy-2x+y=7?\]

Suppose \(x,y\) are real numbers such that \(x+y=20\). What is the maximum possible value of \(x\cdot y\)?

Define a sequence \(S_n\) as follows: Given a starting value \(S_0\), for all \(n\geq 1\), define \(S_n\) as \(S_{n-1}^2\) modulo 10 taken to be a number from 0 to 9 inclusive. For example, if the starting value \(S_0=2\), then our sequence goes \(2,4,6,6,6,\ldots\).

Suppose a random integer is picked as the starting value \(S_0\). What is the probability that \(S_{2017}\) is not divisible by 3?

Master the problem solving skills of Ace the AMC.

Join Brilliant

Problem Loading...

Note Loading...

Set Loading...