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 118
You've been asked to buy the cakes for the school party and you've been given $100 to buy 100 cakes.
Answer
15 donuts, 10 chocolate eclairs and 75 iced rolls.
15 + 10 + 75 = 100 and 15 x 0.56 + 10 x 2.26 + 75 x 0.92 = 100.00.
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Puzzle 119
At the equator the radius of the earth is 6,378 km, so its circumference is almost exactly 40,000 km.
Imagine we had a long rope which went around the equator, this would of course be 40,000 km long.
If we now placed 1 metre sticks vertically all the way around and lay the rope on top of these sticks (so the rope would be 1m higher all the way around) how much extra rope would we require?
