r/mathriddles

You play three tennis matches. You have a 70% chance of beating your teacher in any match and a 30% chance of beating a champion. Assume the results of all three matches are independent, and the win probabilities stay fixed.

Your goal is to win at least two consecutive matches. You can choose one of these orders:

Teacher — Champion — Teacher

Champion — Teacher — Champion

Which order gives the higher probability of achieving your goal, and why? Winning all three also counts as success.

Bonus: if the two win probabilities are any 0 < q < p < 1, is the same choice always better?

Creator disclosure: I run Think in Odds, a daily probability puzzle site. This is a released puzzle version; optional hints and a worked explanation are here: https://thinkinodds.com/puzzles/tennis?utm_source=reddit-mathriddles&utm_medium=reddit&utm_campaign=r_mathriddles_first_players_oct2026

During one of your long journeys, you come across a desolate mountaintop in the middle of nowhere. To your surprise, you are met with a crowd of gods arguing with each other. Upon seeing you, they stop their debate to tell you that they will grant you a wish if you can solve their riddle.​

There are 100 gods in total. When asked a question, 90 of them will always answer truthfully, while the remaining 10 will answer each question randomly. Initially, you don’t know which god falls into which of the two categories, but each god knows it for every other god.

Your goal is to identify at least one truth-telling god using at most 20 yes-or-no questions. Each question can be directed at only one god at a time, though multiple gods can be asked the same question one after another, with each asking counting towards the limit.

Can you come up with a strategy that is guaranteed to work?

(this is a follow up question from this question inspired by u/blungbat)

the image shows 3 rectangular grids on torus, i.e. (Z/nZ)^2 .

each torus is partitioned into two regions. each region is connected and does not contain 2x2 subregion.

unfortunately the second and third grid is partially destroyed. their size is 7x7 and 8x8 in an unknown order.

how many blue tiles are there in each torus?

https://preview.redd.it/xii98zo5gdth1.png?width=457&format=png&auto=webp&s=cc30a626ce476ed0eed660939310869df27a83b3

imagine you have a plane with 4 distinct points named p1, p2, p3 and p4. the gradient between p1 and p2 is -2, and the gradient between p2 and p3 is 1/3. you want p1p3p2 to be 90 degrees and p1p4p2 to also be 90 degrees, with p3 and p4 being on the same side of the line p1p2. find the all the INTEGER solution(s) for all 4 points with the MINIMUM distance between p1 and p2.