**Magic Numbers**

*Puzzles on this Page:*

Divisional Magic

Go 1

Go 2

Here is an interesting conundrum and a great party trick.

Ask someone to tap a random 3-digit number in their calculator or phone calculator, without letting you know what that number is. Ask them to secretly write down the 3-digit number on a separate piece of paper and keep it hidden on their person. Then ask them to repeat the same three digits in the same order to generate a 6-digit number on the calculator or phone.

Ask someone to tap a random 3-digit number in their calculator or phone calculator, without letting you know what that number is. Ask them to secretly write down the 3-digit number on a separate piece of paper and keep it hidden on their person. Then ask them to repeat the same three digits in the same order to generate a 6-digit number on the calculator or phone.

For example, if their first 3 digits are 469 then repeated, the 6-digit number becomes 469469.

Now ask them to pass the calculator to someone else in the room without letting you see the number.

This is where it gets clever.

Say to the new handler of the calculator “Please keep out of sight of everyone else what you are going to do next. I think that the number you have on the calculator is exactly divisible by 13 – could you try that for me please?”

The handler divides in our case 469,469 by 13 and gets 36,113.

“OK” you say, “is that a new whole number with no decimals” and surprisingly, they will agree it is, but they must not tell you the number or show anyone else the calculator screen.

Now say “OK, now I think the number you have left is exactly divisible by 11, could you try that please.” The handler divides the remaining number (in our example 36,113) by 11 and gets 3,283.

“OK” you say “is that a new whole number with no decimals” and again they will agree it is, but as before, they must not tell you the number or show anyone else the calculator screen.

Finally, you say “OK, now I think the number you have left is exactly divisible by 7, could you try that please.” The handler divides the remaining number (in our example 3,283 by 7) and gets 469.

“OK, please confirm that again this leaves a whole number with no decimals.” And they do. Please ask the first person what the number is written on their piece of paper and it will be the same as the number that is left on the calculator. In our example 469 - and it will be, try it for yourself.

If you haven’t fathomed that one yet it is fully explained in the A Hen and a Half book with much more insight and other number magic in the Ahaah eBook.

Let’s give you an example and solution to some simple magic number fun, right here.

Ask one of your Pals to type in any 3-digit number on their phone calculator (or any calculator come to that!).
Obviously without you seeing it.

This must be a number they will remember, so, if need be, get them to jot it down secretly somewhere.

Now ask them to multiply their number by 579.

Now tell them they will have a 5 or 6-digit number on their screen. They will agree.

Now ask them the last 3 digits of that number. And put that number in your phone

You now tell them their original number!

You are right and you win.

Ask your next Pal to type in a new 3-digit number into their phone. No, no you say when they think this is a repeat of the last trick.

Now ask them to multiply their number by 381.

Now tell them they will have a 5 or 6-digit number on their screen. They will agree.

Now ask them the last 3 digits of that number. And put that number in your phone

You now tell them their original number!

You are right and you win.

Can you figure this out? Try a few times on your own and see if you can work out the simple, but mysterious arithmetic going on here!

© Tarquin Group