Beautiful Card Trick - Numberphile

Standup mathematician Matt Parker says this 27-card trick is the most mathematically beautiful - but it takes some explaining!
More links & stuff in full description below ↓↓↓

NUMBERPHILE

Videos by Brady Haran

[mr.champion]

"im gonna call the top pile the zeroth one, the middle pile the first one, and the bottom pile the 2nd one" this proves he's a programmer

[OrigamiPie]

Any coincidence this is the 27th video in the playlist of Matt Parker's Numberphile videos?

[Biskwyy]

The passion, you can see it in his eyes when he explains mathematics. This is a person who loves conversing with the universe.

[gambler]

Loved this trick! I've been dabbling in card tricks for awhile, but this was the first one I learned enough to actually try out on some friends. I added a few elements for the presentation. I split the deck in half (26 in both) then tell the spectator to have a card in mind and then pick either of the decks. I then tell them to go through the deck while I leave the room. If their card is in the half deck they have, they'll place it in the other deck and shuffle, otherwise they place any random card from their deck into the other deck. Either way, the other deck now has one more card and their card (27). Seems complicated writing it out, but it worked well. Then I come back in and perform the trick, doing some cuts while they tell me their favorite number. Probably the only simplification I might make is just tell them to find their card in either deck and then put a random card from the other deck in it, and shuffle. It worked really well and had great reactions.

[DArtagnonW]

This looks like a good place for my favorite number-base joke:

Why do programmers get Halloween and Christmas confused?

Because Oct31 = Dec25

[lloydbotway]

Just wanted to point out (as was noted below by Sonja Quan) that this trick works equally as well with 64 cards. You have to convert the chosen number (number of cards from the top), minus 1, to base 4 using 1, 4, 16 instead of 1, 3, 9, and number the positions in the deck 0 to 3, top to bottom, and deal 4 piles each time (3 times), Otherwise it works the same way. This can be extended similarly to any deck of N-cubed different cards. Other generalizations are possible, if you don't mind dealing LOTS of cards.

[onegamingmoose]

Why don't you set up a shop where you can by the special brown paper?

[DaveMartinCanuck]

love this one, I show it to my students when I can. My Dad taught me this when I was a kid

[draheim]

I don't think this takes a lot of math skill, if I am doing it correctly.

Whatever number they say, subtract 1. So let's say the number is 17.

How many times does 9 go into 16? 1 with 7 leftover
So with that 7 remainder we ask, how many times does 3 go into 7? 2 with 1 leftover
With that 1 remainder, we ask how many times does 1 go into 1? 1

So this gives us 1, 2, 1 In reverse order where 0 = top, 1 = middle, and 2 = bottom, we get middle, bottom, middle, and the card the person selected will be the 17th card in the deck.

[micronalpha]

Great math! But it is also possible to use base 2 and 36 cards, base 3 and 27 cards, base 4 and 16 cards, base 5 and 25 cards, base 6 and 36 cards, base 7 and 49 cards (my favourite!). A great video by Matt! :)

[Mikrobizeps]

It's possible to do it blind folded! LIKE A BOSS!

[joshuaolian]

“do you want to know how it works?”
“yes plea-“
“THIS, this is brilliant”
😂

[CaelenSawyers]

As soon as you said "27 cards" I knew the trick...considering it's the only card trick I've known for years and show it off all the time. Nice seeing it get some recognition.

[legochickenguy]

You can also add the digits together and what group of three the sum is in determines the position, so 1 2 and 3 are the top 3, 4 5 and 6 are the middle 3, and 7 8 and 9 are the bottom 3. Then you find the final position by which group of nine the chosen number itself is in: 1-9, 10-18, or 19-27. For instance, if 25 the chosen number, 2+5 is 7, and 7 is the top number of the bottom 3, and 25 is in the bottom 9, so in the order is top bottom bottom

[Sylocat]

I've thought of a variant. You have to be able to compute numbers in multiple bases though.

Ask the volunteer to pick any number between, say, 10 and 52, that isn't prime (call this number X). Then ask them to pick any divisor of X (call this number Y). Then ask them to pick their favorite number between 1 and X (call this number Z). Then do this trick with X cards sorted into Y piles each time, with the card ending up in position Z.

[danturney]

Great trick - thanks! (5 years later) Tried this on two people - both impressed, but both said they knew it involved what order the card piles were picked up but couldn’t see a pattern. I would add one more twist (maybe it’s been offered in the comments already): Make a mental note of the remainder when you divide their number by 9 (if it’s 0 then make it 9 instead). This will be the “triplet” where their card appears when you lay them down the third time. Let’s say they choose 16 (so the remainder is 7). When you lay down the 7th triplet (i.e., the 19th, 20th, and 21st cards) on the third pass try to memorize those three. Then when they point to the pile it’s in you’ll know which of those was their card. Then as you count out the cards up to their chosen number just pause before turning it and ask “was it the 5 of hearts?” and then turn it over.

[MicrocosmicExperience]

When he said he was memorizing each pile's content every time. I was thinking, 'Wow, that seems like a simple card trick everyone can do."

[knocknockify]

A few summers ago, my cousins and I learned some card tricks and taught them to each other. I had learned this trick by watching this video. It's been so long now, I've forgotten how to do this trick, but watching this video again brought some great/fun memories

[Edsel]

There are two variations of this that I've used at work. One is to use a variation of the method from James' "Brown criterion" number selection video to get the person's number and then do the trick. The other is to use the first letter of the person's first name and use A=1, B=2 etc. to choose where the card goes, since 26 letters work well with 27 cards. When you're dealing off dummy cards at the end use letters instead of numbers, e.g. "A, B, C, D ... Q, R, S, T for Tony" and show the card.

[imagecaster]

always love watching and listening to Matt Parker's vids... makes them interesting