Problem

AMC Practice #1 - Problem 8

Alex and Alvin are playing a game with $N$ slots. Every turn, Alex can either place $1$ coin in $2$ slots, or $2$ coins in $1$ slot. Then, Alvin can remove all the coins from $1$ slot. What is the minimum $N$ such that no matter what Alvin does, Alex can form a stack of $10$ coins in $1$ slot at some point in time?

Show/Hide Problem Tags

Problem Tags: Game theory

Want to contribute problems and receive full credit? Click here to add your problem!
Please report any issues to us in our Discord server
Go to previous contest problem (SHIFT + Left Arrow) Go to next contest problem (SHIFT + Right Arrow)

Problem feedback

Difficulty —

Category: AMC Practice #1
Points: 3
Back to practice
Train more like this