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Imagine the worst luck that Rachel could have.
She could take out all 3 socks with holes in them before she finds a pair.
If all of the white socks or all of the blue socks have holes in them, then having removed the socks with holes in them, Rachel will only have socks of two colours left, which will speed the process up.
So if Rachel is unlucky, there will still be socks of all 3 colours left after discounting the socks with the holes in them, and she will use up 3 choices taking a sock of each colour. Then, the 7th sock will have to make a pair with one of them.
So the most choices that Rachel could need is 7.
Counting Socks
Age 11 to 14
ShortChallenge Level 
Imagine the worst luck that Rachel could have.
She could take out all 3 socks with holes in them before she finds a pair.
If all of the white socks or all of the blue socks have holes in them, then having removed the socks with holes in them, Rachel will only have socks of two colours left, which will speed the process up.
So if Rachel is unlucky, there will still be socks of all 3 colours left after discounting the socks with the holes in them, and she will use up 3 choices taking a sock of each colour. Then, the 7th sock will have to make a pair with one of them.
So the most choices that Rachel could need is 7.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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