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Understanding Math Beyond the Classroom
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How it Works › Forums › Introductory Problems (AMC 8 Problems 10-20) › Combinatorics on the Grid Introductory Problems!
This topic contains 0 replies, has 1 voice, and was last updated by Ayush 2 years, 9 months ago.
Here are the introductory problems for the next week! These are more difficult than AMC 8 Problems but you can make progress on them if you attended the lecture. Each of these problems is worth 5 points to your leaderboard score! If you don’t understand one of the questions, feel free to post in the questions forum here.
1. The confused boy BobJoe is lost on the coordinate plane. He starts off at (0, 0) and at
each minute he moves randomly one unit right, left, up, or down. What is the probability
that after 4 minutes he is back at the origin? 6 minutes? Why did I not ask about 5
minutes?
2. What is the maximum number of rooks you can place on an 8-by-8 grid such that no
two rooks are attacking each other? (Two rooks attack each other if they are in the
same row or column) Similarly, how many bishops can you place on an 8-by-8 grid such
that no two bishops attack each other? (Two bishops attack each other if they are on
the same diagonal)
3. Tom and Jerry are playing a tic-tac-toe game on a 2×2 grid where Jerry makes the first
move. How many sequences of moves end with Jerry winning the game? How many
sequences end up with tom winning the game? Can we generalize to an n-by-n grid?
Remember that you can post your solutions below to these problems and I will keep a running leaderboard for the top 10 students who participate the most! I especially appreciate the same problem being solved in different ways!