User:Bluefire272/Explanations and other crap

About this page

This is a page I use to publish explanations and formulae for both Uncyclopedia related and unrelated content. If you want to ask me anything, please do so here.

Math card trick

I am quite fond of mathematical card tricks, but I hate it when people publish them and don't explain how they work to others, and even worse, pretend that they don't know. I think that if you want to publish a trick on the internet where anyone can see it and comment on it, you need to publish at least a hint, and you don't have the right to complain when someone like me comes along and tells everyone how it's done if you haven't already. So here goes. The trick in question is here and the answer is below:

So we start with selecting 3 random cards. then we make 3 piles of 10, 15 and 15 cards, leaving us with 9 (3+10+15+15+9=52). Then we place one of the selected cards on top of pile 1 (15 cards), and then cut a bit off pile 2 (15 as well), let's call that bit a, and let's call the remainder in pile 2 b. Note that a+b=15. Then, we repeat, so place the second selected card on the remainder of pile 2 (b), and cut off a chunk of pile 3 (consisting of 10 cards) and place it on what's left of the second pile (the second selected card on top of b cards). Let's call the bit we just took off pile 3 c</am> and the cards left in pile 3 d. Note that c+d=15. Then we place the remaining 9 cards (I hope you remembered them) on top of the new pile 3 (d and the third selected card). Then pick up the new new (yes there are meant to be 2 "new"s) third pile and put it on the new second pile, and put them both on the new first pile. This is the spacing in the pack at this point (starting from the top, where the new new pile 3 should be):

9 cards, S3, d cards, c cards, S2, b cards, a cards, S1, 10 cards. (S stands for selected card; so S1 is selected card 1)

But as we know that c+d=15 and a+b=10, we can now substitute in those values (because a and b are next to each other, and so are c and d, and get this:

9 cards, S3, 15 cards, S2, 15 cards, S1, 10 cards.

This is a LOT simpler to deal with. Also notice that the intervals are...9, 15, 15 and 10! So it's as if we didn't do any cutting, in fact that bit is only to enchance the trick.

Then, we take 4 cards from the top (so from the 9 cards section), and put them on the bottom, to get this:

5 cards, S3, 15 cards, S2, 15 cards, S1, 14 cards.

The fact that 5 and 15 are odd numbers is crucial in what happens next. Why? Because when we start alternating cards in the next step, things will get sticky if we don't have odd numbers as the first 3 intervals. It is also crucial that we start with UP. This bit is quite complicated to explain in words but easy to understand for yourself, so I'll just tell you what you end up with and if you want to figure out why (which isn't too hard to do as I just said) then please do so. So anyhow, after the first round of updownupdown, when we take away all the cards in the UP pile, we are left with this:

2 cards, S3, 7 cards, S2, 7 cards, S1, 7 cards.

As you will see if you figure it out yourself, the odd 5 and 15s make sure that the selected cards go to the DOWN pile. Now this is the bit where I nearly got stumped. As you can see the first number is 2. But 2 is an even number... I then realized that because when you do the updownupdown thing, you take off the top card FIRST, and the bottom one LAST, the whole pile gets reversed. So:

7 cards, S1, 7 cards, S2, 7 cards, S3, 2 cards.

7 is of course odd. Repeat the previous step to get:

3 cards, S1, 3 cards, selected card 2, 3 cards, S3, 1 card. Flip to correct:

1 card, S3, 3 cards, S2, 3 cards, S1, 3 cards.

Repeat yet again, to get (flip included):

1 card, S1, 1 card, S2, 1 card, S3, 0 cards.

Note that the last section is now zero, so we can ignore it:

1,S1,1,S2,1,S3.

Do updownupdown to get... guess what? S1, S2, S3! Congratulations if you got it, if you didn't keep trying. If you didn't understand this, contact me by leaving a message at my talk page here, I'll be happy to explain. Also contact me if you want another trick explained.