Reasoning
By likely, we mean greater than 50% chance.
With one person there is a 0 percent chance that you'll have two people with the same birthday.
With two people the probability that they won't share a birthday is 364 ÷ 365. The probability that they will share a birthday is therefore 1 − (364 ÷ 365).
With three people the probability that they won't share a birthday is the same as for two people, times 363 ÷ 365. So the probability that three people will share a birthday is 1 − (364 ÷ 365) x (363 ÷ 365).
Notice that with each additional person added, the probability that they shares a birthday with one of the previous persons goes up, because there are fewer "free" days remaining.
We keep adding people until the %age is greater than 50%.
When we have 23 people the %age is 50.729%.
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Puzzle 479
Would you believe that this amazing sentence contains ninety two letters, one comma and a single question mark?
Answer
This is not really a puzzle, merely a curious piece of text.
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Puzzle 480
Start in square 'S' and end in square 'E' moving either horizontally or vertically in each move. Start by moving 2 squares in each of your moves, but when you land on a '*' square, change the number of squares you move from 2 to 3, or vice versa. You can not step on or pass through the black squares and you have only 8 moves in which to complete this task.
