The book The Founders by Jimmy Soni tells the story of the Paypal Mafia – the tech bros who founded and ran the online payments company.
The most famous of this troupe – Elon Musk, Peter Thiel and David Sacks – are now as well known for their Trumpist politics as their entrepreneurial ingenuity. Back in the day, however, what really got their blood pumping was mathematical puzzles.
Soni’s book mentions these three questions, which became staples of the Paypal job interview. Are you smart enough to become a rightwing billionaire?
1. Divide and conquer
Whole numbers either have an odd number of unique divisors or an even number. Which whole numbers have an odd number of divisors?
[A divisor of Z is a number that divides into Z. For example, the divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. There are thus eight unique divisors of 24.]
2. Rope-a-dope
There are two ropes each of which’s density varies along its length such that they burn at different rates at different positions along their lengths, but each takes one hour to burn fully. How would you use the two ropes to measure 45 minutes?
3. Coin conundrum
There is a circular table of unspecified diameter. You and your opponent have a supply of identically-sized coins. The game is for you each to place a coin on the table in turn. No coin can be moved after placing and no coin can be placed wholly or partially on top of another. The first player unable to place a coin loses. What is your strategy to ensure you win?
I’ll be back at 5pm UK with the solutions.
PLEASE NO SPOILERS. Instead, please talk about ropes and coins.
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.