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How to perform the trick:
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+ - Ask someone to pick a secret number between 1 and 31
+ - Show them the 5 cards below and ask them to tell you which cards contain their number
+ - Add up the first numbers (16, 8, 4, 2, 1) from the cards they selected
+ - The sum will be their secret number!
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Why does it work?
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+ This trick is based on binary number representation. Every number from 1 to 31 can be expressed as a sum of powers of 2: 16, 8, 4, 2, and 1.
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+ Each card contains all numbers that have a "1" in a specific binary position:
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+ - Card 16: Numbers with 1 in the 16's place (binary position 4)
+ - Card 8: Numbers with 1 in the 8's place (binary position 3)
+ - Card 4: Numbers with 1 in the 4's place (binary position 2)
+ - Card 2: Numbers with 1 in the 2's place (binary position 1)
+ - Card 1: Numbers with 1 in the 1's place (binary position 0)
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Example:
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The number 19 in binary is 10011, which means 16 + 2 + 1 = 19
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So 19 appears on cards 16, 2, and 1, but not on cards 8 or 4.
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+ When you add up the first numbers from the selected cards, you're reconstructing the binary representation of their secret number!
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