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Past Problems of the Week

Join our Discord server to submit your answers for the competition here: https://discord.gg/v32fxjUbgn 

2/15 - 2/21 POTW

A box contains 6 red, 4 blue, and 4 green marbles. If 6 marbles are taken out, what is the probability that at least 1 marble of every color was taken out?

Written by Adwita Mandiwal

2/01-2/06 POTW

Joe is playing a game with infinite cups where he wants to maximize the number of points he earns. Joe plays by tossing ping pong balls into cups, starting with cup 1, and continues until he misses. He makes each shot with 1/3 probability, and the number of points he earns is i, where the (i+1)th cup was his first miss. What is the expected number of points he earns? Express your answer as a common fraction.

Written by Aashita Mandiwal

1/25 - 1/31 POTW

Seven balls are numbered 1 through 7. There are three buckets; one red, one green, and one blue. How many ways are there to put them into the buckets such that no two consecutively numbered balls go into the red and green buckets, no three consecutively numbered balls go into the blue bucket (but two consecutively numbered balls can), and the blue bucket can't be empty?

Written by Elaine Zhou

1/18 - 1/24 POTW

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Written by Adwita Mandiwal

1/11 - 1/17 POTW

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Written by Sophia Jin

1/04-1/10 POTW

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Written by Thanishkka Vijayabaskar

12/28-1/03 POTW

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Written by Avery Xu

12/21-12/27 POTW

Written by Adya Garg

12/14-12/20 POTW

Written by Fiona Liu

12/7-12/13 POTW

Let ABC be a triangle with ∠A = 20°, ∠B = ∠C = 80°, and BC = 2025. Let P be a point on side AC and let Q be a point inside â–³ABC such that AP = PQ = QB and PQ || AB. Find the value of this common length.

~ Written by Ivy Guo (MA4G 2025)​

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