Hint: Think about the first digits of the numbers.
There are more 2s because of the numbers beginning with 20,000.
I have a drawer full of socks.
There are 5 socks of each colour, red and green, evenly mixed.
In the morning, when it is very dark, I need to pull out a pair of socks of the same colour.
How many must I pull out of the drawer to ensure that I have at least one pair of matching socks?
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Hint: It's not at many as you think.
Answer: Three socks.
Once we have 2 socks, then any other will form a pair.
Mr Smith has lots of pound coins, ten boxes in all. Each box contains 100 pound coins, but one box contains coins which are all counterfeit and are slightly lighter, 1/16 of an ounce lighter to be exact.
The problem lies in the fact that they all look identical, the only way to tell them apart is to weigh them.
Mr Smith knows the correct weight for a box, but how many weighings are required to determine which box contains the counterfeit ones?
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Hint: The answer is a lot less than 100 weighings.
Answer: One weighing is enough.
Take one coin from the first box, two from the second and so on.
When the coins are weighed, the number of 1/16ths light will tell us which box contains the counterfeits.
For example if it was box 5, the weighing would be 5/16 too light.
What day would tomorrow be if...
...yesterday was five days before the day after Sunday's tomorrow?
"five days before the day after Sunday's tomorrow"
is therefore Thursday.
"yesterday was five days before the day after Sunday's tomorrow"
yesterday was Thursday, making today Friday. Therefore tomorrow is Saturday.