Monday puzzle: pairs of cards
Let's play a game of chance. I have in my hand a standard 52 card deck. What I will do is flip over two cards at a time. If the two cards happen to be red, then you get the pair. If the two cards are black, then I get the pair. ...

Monday puzzle: Excel random numbers
The Excel function rand() generates a random number between 0 and 1. Let's say I generate two numbers using the rand() function. What is the probability the two numbers sum is less than 1 AND their product is less than 3/16? Give it a try, or experiment numerically, before reading the answer after ...

Monday puzzle: random music
Have you ever felt your iPod or music player's shuffle function was not working correctly? Today's problem is about how random events are not always perceived as random.

Monday Puzzle: Alice and Bob race to 1 million
This is a fun game in which Alice and Bob race to 1 million in a mathematical sense. Alice and Bob start with the number 1. Alice multiplies 1 by any whole number from 2 to 9. Bob then multiplies the result by any whole number from 2 to 9, and ...

A math game of dodgeball
Let's analyze a math game called dodgeball that's a sort of twist on tic-tac-toe. Here is how the game works. It's a two player game with the following set-up. Player 1 gets a 6x6 grid of squares as follows: Player 2 gets a 6x1 grid of squares: Here are the rules: 1. Player 1 begins ...

Puzzle: who wins this dart game?
Alice and Bob play the following game with their friend Charlie. Charlie begins the game by secretly picking a spot on the dartboard. The spot can be anywhere on the board, but once picked it does not change. Then Alice and Bob each get to throw one dart at the board. At this ...

Monday puzzle: train station pickup
This is a fun little puzzle about commuting from the train station. Mr. Smith, a commuter, is picked up each day at the train station at exactly 5 o'clock. One day he arrived at the train station unannounced at 4 o'clock and began to walk home. Eventually he met the chauffeur ...

Monday puzzle: elevator buttons malfunctioning (spoilers)
An elevator in my office building of 65 floors is malfunctioning. Whenever someone wants to go up, the elevator moves up by 8 floors if it can. If the elevator cannot move up by 8 floors, it stays in the same spot (if you are on floor 63 and press up, ...

Puzzle: how would you divide the land equally? (spoilers)
While I normally post math puzzles on Monday, I found another interesting puzzle so there is a bonus problem this week. Here is the problem. A father dies and wants to divide his land evenly amongst four sons. The plot of land has the following unusual shape: How can you divide the land ...

Monday puzzle: paying an employee in gold
In honor of Labor day, I thought I would offer the following interview brain teaser as today's puzzle. You have a solid gold bar, marked into 7 equal divisions as follows: | - | - | - | - | - | - | - | You need to pay an employee each ...

Probability puzzle: what are the odds of a bad password?
The other day I got an email about an interesting probability problem: Hi Presh - I'm a regular reader of your site and I came across a question which has bugged me the last couple of days. The problem is as follows: A system has 100 accounts, two of which have bad ...

Math puzzle: chances of meeting up with a friend (and game theory puzzle extension)
Some nights that I go out to the bars it seems like I end up running into everyone. Other nights it's the exact opposite where I get out of sync and miss meeting my friends. The dynamics of meeting friends is rather interesting, and here is a probability puzzle that captures ...

Birthday laws probability puzzle
Wouldn't it be fun if you could get a holiday every year on your birthday? Wouldn't it be even better if your friends got the same holiday too? Such a labor law would make for some fun parties. But it might have some interesting macro effects on the economy as a whole. Here's ...

Video roulette math puzzle
I recently heard of a game called Netflix roulette where people pick a video at random and watch it regardless of the result. It got me thinking about probability and I came up with the following problem. Bob loves the TV show Law & Order. Each day he picks an episode at ...

The Patriarch’s Will – a game theory puzzle
Long-time reader Scott found the following puzzle from this site: Here is a scenario which occurred many millennia ago: The patriarch of a wealthy family was on his deathbed and wanted to divide his gold among his eight sons who were all very, very greedy. Wishing to favor the oldest son (as ...