All of the number pairs that have the same sum line up along the same diagonal line, as shown by the arrows.ġ. As shown below, we only need to consider one triangular half of this table since the order of the numbers doesn’t matter. Within each cell we can put both the sum and the product separated by a comma, as first described by Dabed. The best way to do so is to create an 8-by-8 table with the numbers 2 to 9 on both axes. This seems like magical mind reading at first glance - where could they be getting the new information to solve the problem? Can you figure out the two numbers (there are two possible answers)? Can you explain how S and P did this?įirst, we tabulate all the possible sums and products. S: Aha! Now I know what the two numbers are! S: I cannot deduce what the two numbers are. Both S and P know everything we’ve just specified. S is given only the sum of the two numbers, and P is given only the product. S and P are two mathematicians with perfect logic. The two numbers can include 2 or 9 and they can both be the same number. There are two unknown numbers between 2 and 9. As George commented, for a four-digit number you’d have to multiply by 73 and 137. The information that makes the trick work is the fact that the number has three digits. That this will produce a copy of the original three-digit number (say, 457) is obvious when you write down the multiplication in the conventional way. The reason, as many readers correctly pointed out, is that 7 × 11 × 13 = 1,001, which is the number that you are effectively asking the child to multiply by. The question for you, or for an older child, is - why does this work? If the child has done this right, you might find a smile start to light up their face. Finally - and at this point you can add feigned concentration and appropriate magical phrases - ask them to multiply the second answer by 13. Then ask them to multiply the answer by 11. Then tell them that you will reveal the number by producing two copies of it side by side! First ask the child to multiply their number by 7. Our first puzzle was an elementary arithmetic trick suitable for captivating a child:Īsk the child to think of a three-digit number without telling you what it is. But how does the magician correctly deduce what’s in your mind based on seemingly no information? As we’ll see below, the secret is to extract just enough information to unravel the mystery through the inexorable logic of mathematics. The tricks in question were of the sort where the magician somehow divines the identity of your hidden numbers or playing cards. In our most recent Insights puzzle, I challenged readers to figure out how certain magic tricks work.
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