Birthday Bet

Copyright 1997 by Paul Niquette. All rights reserved.


Birthday CakesYou are seated with a statistician in a small restaurant. Suddenly your conversation is interrupted by singing. A quartet of waitpersons are gathered around a nearby table, where sits a blushing guest grinning at a cake festooned with candles. "Happy birthday to you..."
    Your friend is preoccupied, silently pointing at persons all around the restaurant and counting them.
"Care to make a wager?" asks the statistician. "I will pay for your meal if you can show me that at least two people in this room have the same birthday."

Ah, but you, too, are a person sophisticated with numbers. It is your turn to do some counting.

    There are four tables with two persons and two tables with four persons.
Your companion watches while you make solemn calculations on your napkin.

"Pay up," you say, handing your check across the table.

"Not so fast," says the statistician, now grinning. "Unless you have asked every person in the restaurant for their birthdays, you cannot possibly know that you have won."

"With enough people in the room, it's a good bet" you say with a shrug. "Go around the room and do the asking yourself. You will be embarrassed, but you will see that I win."

"Probability theory predicts that you will lose," your friend protests. "Even counting the restaurant staff, you obviously have too few present for even an even bet."

"Maybe so, but I have this," you say, taking a card out of your wallet.

The statistician stares at the card and grimaces. "You are a scoundrel," she says, taking a card out of her purse.

What was on the two cards?