2 Insiemi numerici e operazioni elementari 2. After having counted 5 cards from the top of the 4. Before having your friend repeating the step, put original deck, he/she memorizes the fifth card, which, for example, is three of clubs. the five cards previously removed on the top of the deck so that when the 14 cards are taken out to perform again the operation, the last 5 cards used in the precedent counting will actually be left over. 3. Now let us imagine that the celeb s name is Galileo Galilei which has 14 letters. By showing your friend how to do it, you put one card upon another and spell the name G-a-l-i-l-e-o-G-a-l-il-e-i, thus inverting the card order. When you place them back to the original deck, the three of clubs is no more occupying the fifth place but it is fifth from last of the 14 cards taken out. ESERCIZI 5. The three of clubs, which was the fifth from last of the 14 cards, is now the first of the 5 cards left over. That is the card next to the ones removed the second time. Let us point out the inverse operations we are using. At the beginning, we are taking out 5 cards from 14 that is: 14 5 Hence, the card our friend will look at is occupying the tenth position: (14 5) + 1 = 10 Then, we add the previously removed 5 cards on the top of the deck: [(14 5) + 1] + 5 = 10 + 5 = 15 After the celeb s names spelling, we take out 14 cards from the deck: {[(14 5) + 1] + 5} 14 = {10 + 5} 14 = 15 14 = 1 This result equals the place occupied by the card chosen by our friend. If we write the expression without its parentheses, the inverse operations become more evident. In fact: 14 5 + 1 + 5 14 = +1 Now, it s your turn 1. Does the game work if the number of the removed cards is greater than the celeb s name total characters? .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... 2. Why the number of cards removed at the beginning cannot be greater than 10? .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... 147