In a group of 23
people there are 253
possible pairs. Mathematician
Warren Weaver's book
Lady Luck relates an interesting story about this curious fact.
During World War II, a number of officers gathered for a dinner party, and this old chestnut became the topic of conversation. Few of Weaver's fellow guests believed that the number could be as low as 23; after all, it defies common sense that the number would be below 100. Eventually, someone pointed out that 22 people were seated around the table, and the theory was put to the test. Each of the guests revealed his birthday, but there were no matches. Suddenly, the waitress spoke up:
"Excuse me. I am the 23rd person in the room, and my birthday is May 17, just like the general's over there."