Brainteasers
Brainteaser – A Perfect Split
You have a set of coins (11 or more) where 10 are tails up and the rest are heads up.
You are blindfolded and the coins are shuffled on the table.
How can you divide the coins into two groups where both have an equal number of tails?
Note: you can’t tell by feeling the coins which side is up.
Show Answer
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Separate out any 10 coins from the pile (it doesn’t matter which 10, since you are blindfolded and cannot distinguish heads from tails).
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Flip all those 10 coins over.
Here’s why this works:
- Suppose in the 10 coins you picked, there are 𝑥 tails.
- Since there are a total of 10 tails in all the coins, the other pile (everything you did not pick) must have 10 − 𝑥 tails.
- By flipping your chosen 10 coins, those 𝑥 tails become heads, and the remaining (10 − 𝑥) heads become (10 − 𝑥) tails.
- After flipping, your chosen 10-coin pile now has (10 − 𝑥) tails – exactly the same number of tails as in the other pile.
