Archives
Here you can see the archives for the Euclidean Math Circle's Problems of the Day (PotD). Enjoy solving!
April 22, 2021
Find the number of positive integers less than 1000 that can be expressed as the difference of two integral powers of 2.
2021 AIME I # 3
Solution
April 21, 2021
Zou and Chou are practicing their 100-meter sprints by running 6 races against each other. Zou wins the first race, and after that, the probability that one of them wins a race is 2/3 if they won the previous race but only 1/3 if they lost the previous race. The probability that Zou will win exactly 5 of the 6 races is m/n, where m and n are relatively prime positive integers. Find m+n.
2021 AIME I # 1
Solution
April 20, 2021
Abe holds 1 green and 1 red jelly bean in his hand. Bob holds 1 green, 1 yellow, and 2 red jelly beans in his hand. Each randomly picks a jelly bean to show the other. What is the probability that the colors match?
2013 AMC 8 #14
Solution