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 7
Moving from letter to letter using the moves of a chess knight, can you find the letters 'PUZZLES' in order?
Z
E
Z
S
Z
P
S
U
P
S
P
L
P
Z
S
U
L
U
U
E
U
E
E
P
U
S
U
P
P
Z
L
L
U
P
Z
Z
U
Z
S
U
L
P
E
P
Z
Z
E
L
U
Note: this puzzle is not interactive, and the squares cannot be clicked.
