Jamshrivelson

Question: You’re making a sign using a marker to draw the letters. The marker tip is a circle that’s $2\text{ cm}$ across. If you want the marks to be as uniform as possible (as measured by the standard deviation of the ink intensity), and you can’t place the tip within $1\text{ cm}$ of where it’s previously been, how far apart should you make the marks? [Solution]

Question: In one of the greatest disasters in the history of collective planning, all 330M residents of the U.S. join the same Zoom call by picking two random times between 8:00 and 9:00. They dial in at the earlier time and hang up at the later time. What is the probability that there is at least one person who is on for some portion of everyone else’s call, a so-called Superzoomer? Further, what is the chance of there being two Superzoomers on the same call? [Solution]

Question: Find the longest words that share letters with only 49 of the 50 U.S. states. Extra: find the state with the most such words. [Solution]

Question: A post can accumulate spam comments, and each spam comment can accumulate spam comments. If each open reply thread accumulates spam at a rate of $1$ reply per day, then what is the expected number of spam posts by the end of a three day weekend? [Solution]

Question: You can make 100 coin flips with either of two coins, Coin A worth $\pm1,$ and Coin B worth $\pm2.$ You survive if you end up with a positive score. How should you flip the coins to maximize your chances? [Solution]

Question: The NYTimes has a new word game called Spelling Bee. The idea of the game is, on a board like the one below, to make words using only the letters on the board under the constraint that the central letter must be used. Words are worth their length in letters (with a minimum length of $4$), but words that use all $7$ letters — known as pangrams — are awarded $7$ bonus points. The valid word list is Peter Norvig’s which contains some 172820 distinct words. The object is to find the game board with the highest possible maximum score. [Solution]