SIG (Susquehanna) Interview Questions

Aaron, Bryce, and Craig are all of different integer ages. They had the following conversation: (i) Bryce to Craig: 'You're the youngest.' (ii) Aaron to Bryce: 'Your age is exactly 70% greater than mine.' (iii) Aaron to Craig: 'Your age is the average of my age and Bryce's age.' (iv) Craig to Aaron: 'I'm at least 8 years older than you.' However, not all of these statements are true. Whenever speaking to someone older, a speaker always tells the truth; when speaking to someone younger, a speaker always lies. How old is Craig?

Mickey and Minnie plan to meet at a cafe, but each will independently arrive at a uniformly random time between 9:00 and 10:00. Mickey will wait 10 minutes for Minnie before leaving, and Minnie will wait 30 minutes for Mickey before leaving. What is the probability that they meet each other?

Given 5 fair dice, what is the probability of obtaining a result where exactly 3 of the dice show the same value?

For a fair coin, what is the minimum, maximum, and expected (average) number of flips needed to get either 3 heads or 3 tails?