Cards N' Such

I'm reading through random articles and here's an interesting one from the Department of Mathematics and Statistics at Stanford University:

"The way that a magic trick works can be just as amazing as the trick itself. My favorite way of illustrating this is to talk about shuffling cards. In this article, I will try to explain how there is a direct connection between shuffling cards and the Riemann Hypothesis — one of the Clay Mathematics Institute’s Millennium Prize Problems. Let us begin with perfect shuffles. Magicians and gamblers can take an ordinary deck of cards, cut it exactly in half, and shuffle the two halves together so that they alternate perfectly as in figure one, which shows a perfect shuffle of an eight-card deck.


If the shuffle is repeated eight times with a fifty-two card deck, the deck returns to its original order. This is one reason that perfect shuffles interest magicians." - Persi Diaconis, Professor of Statistics and Mathematics, Stanford University

Mod Sum Does It All - Part I

I modified a mathematical trick that is a favourite amongst some, well, I like to call them Mathemagicians! And it goes like this:

First, pick out a three digit number, any one will do, that has its digits in decreasing order. Now remember this number, don’t tell me what you have with you.

Second, reverse the order of that number. Then subtract this new number from the original number you thought of. Having done this, remember also this new number that you’ve obtained via subtraction.

Finally, reverse this new number and add to itself.

Well, you have obtained a very, very, very special number! And because it’s so special, I know what it is already, because it’s simply 1089!

And of course this isn’t the trick, because now I’m going to up the difficulty level of this trick and impress you some more; I’m going to give you a range of numbers to choose from, and I’ll say this before hand: ‘the larger the number you choose, the harder it’ll be for me’. So here goes:

54, 1089, 3060, 42012, 80001, 103410, 500031

Now, just choose any one of the above numbers (don’t worry, they aren’t that special actually, I could give you one whole list of other numbers!). Have you chosen one yet? Well if you have, I’m going to up the difficulty one more time!

I want you to choose any number you want, any number with any number of digits, and I want you to multiply your chosen number by that new number you just chose. To make it really hard for my, I implore you to multiply it by say, a 3 digit number.

Now, if you’re trying this out, you’ve to tell me one thing, and I’ll tell you one thing in exchange:

If you tell me all the digits of your final number, save for one, I’ll tell you the last digit you left out.

I’m going to up the difficulty for myself again: you needn’t tell me the digits of your number in order and you can jumble them up. Still, I can tell you the last digit which you didn’t tell me.

Try it! And then you can always come ask me and challenge me, or just tag on the tagboard on the right. :)