Counting coins in the dark

A bunch of coins are in a dark room. Someone tells you how many coins there are, and how many of them are Heads. You’re allowed to flip coins over. How can you make 2 piles of coins, each with the same number of Heads?

Justin Pearson

- Graduate Student Researcher
- Electrical and Computer Engineering
- University of California
- Santa Barbara, California, USA
- justin.pearson @gmail.com

Puzzles

Counting coins in the dark

A bunch of coins are in a dark room. Someone tells you how many coins there are, and how many of them are Heads. You’re allowed to flip coins over. How can you make 2 piles of coins, each with the same number of Heads?

Boarding a plane

100 passengers board a 100-seat airplane. They all have assigned seats, but the first passenger on board instead selects a seat at random. Each subsequent passenger tries to sit in their assigned seat, but if it’s occupied they’ll pick a seat at random. What’s the probability the last passenger sits in his assigned seat?

Lemmings

One hundred lemmings are spaced 1-meter apart on a 101-meter plank in the water. You pick the initial direction of each lemming; each moves at 1m/s until it hits another lemming, at which point they each reverse direction. When all the lemmings are in the water, the game is over. Choose the initial directions of the lemmings to make the game last as long as possible (at least one lemming still on the plank).