There are 7 coins laid on a table with the heads up, and 30 coins laid with the tails up. Each coin has a head side and a tail side. How can you split the coins in two piles, with your eyes closed, so that the piles have the same number of coins with the tails up?
Teacher tip
Use logic puzzles at your classes to increase the motivation and to exercise the flexibility in mathematical thinking.
Solution
First, split the coins, randomly, in two piles with 7 and 30 coins respectively. Let us denote by \(n\) the number of coins in 7-pile with the tails up, which means that there will be \(30 - n\) coins in 30-pile with the tails up. Now, flip all 30 coins in the second 30-pile. You will get a 30-pile with \(n\) coins with the tails up (the same number of coins with the tails up, as in the 7-pile).
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