



 
Any number minus the sum of its digits gives a multiple of 9. And the sum of the digits of a multiple of 9 is again a multiple of 9. So the magician will pick a number so that the four numbers add up to 9. Most of the times, there is only one way to go, and the magician is sure to get it right. However, if the three digits already add up to 9, the magician cannot be sure whether the fourth digit is a 0 or a 9, so he will have to take a guess and hope he's right. For instance, If I pick 2001, I get 20013 = 1998 and I can say 1, 9, 8 to the magician. He's supposed to guess the last 9. But If I had picked 1101, I'd have gotten 11013 = 1098 and I could have said 1, 9, 8 to the magician. That time he would be supposed to guess 0 rather than 9. You can search our database with the keywords casting out nines to find other similar tricks. Claude  


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