Answer: 38 tonnes of chicken feed, 34 tonnes of pig feed and 28 tonnes of cattle feed.
How many people must be at a party before you are likely to have two having the same birthday (but not necessarily the same year)?
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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) * (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%.
In the local wood there are a number of trees. On these trees there are a number of birds.
The local game keeper knows that there are as many birds on each tree as there are trees in the wood.
He also knows that there are between 2000 and 2100 birds in total. How many trees are there in the wood?
We are after a number whose square lies between 2000 and 2100. 45 is the only such number.