I Wonder What's on the Other Side...
There are 10 cards, and each side of each card is a letter from A, B, C, D, and E. All cards have 2 different letters and all cards are distinct. You can see one side of each card, as shown in the diagram. You are to choose a number of cards to flip over. At least one of the cards you flip over must have an E on the other side. What is the least amount of cards you must flip over to be guaranteed to get an E on the other side? (You choose which cards to flip over.)
Note: There is no front side or back side for a card. So, a card that has A on the front side and B on the back side is the same as a card with B on the front side and A on the back side.
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The 4 cards in the top row have to be AB, AC, AD, and AE, although not necessarily in that order. That means that the cards in the second row must be BC, BD, and BE, since the BA card is in the top row. So, the cards in the third row are CD and CE, since CA is in the top row and CB is in the second row. Finally, the card in the bottom row must be DE because DA is in the top row, DB is in the second row, and DC is in the third row.
Therefore, you can flip over the card showing D and the other side will be an E, meaning the answer is 1 .