Card Trick with 9 Cards
Nine cards, three piles, and you spell their card out of the packet. Every card name in the deck works.
Spell it out
Be the spectator and the page does it to you. Be the magician and you gather and spell it yourself.
As the spectator you pick a pile and remember its bottom card, and the page gathers and spells. As the magician it thinks of the card and you decide where their pile goes — which is the one step that can ruin this trick, so it stops you if you get it wrong. The gold ring follows the card being remembered, so you can see where each word puts it. The nine cards are drawn fresh from a shuffled deck every time, so nothing is arranged in your favor. The tracker under the table is the position of the card you are remembering, counted from the top of the packet. It reads 3, then 7, then 5, then 5 — and it reads that whatever card you picked, which is the whole trick.
There is no setup, no sleight, and nothing to memorize. Any nine cards will do and anybody can shuffle them first.
Also called the nine card problem, the 9 card trick, or the 3x3 card trick. It is Jim Steinmeyer's, first published in MAGIC Magazine in May 1993 and reprinted in Impuzzibilities in 2002 — which he still sells from his own shop, and it is worth having. The reason it is called a problem rather than a trick is that the interesting part is proving it cannot fail, and Breeanne Baker Swart and Brittany Shelton did exactly that in Mathematics Magazine in 2015.
How to perform it
- Count off nine cards. Any nine. Let them shuffle first if they want to — it makes no difference.
- Deal three piles of three, across. One card to each pile, then round again, until all nine are down.
- Have them pick a pile and look at the bottom card of it. That is their card. You never see it.
- Drop their pile on top of the other two. Their card is now third from the top of the nine. This is the only thing in the whole trick that has to be right, and it is the step people get wrong — put their pile underneath or in the middle and nothing that follows works.
- Ask them to name their card out loud. They can, because knowing it does not help you. That is what makes this one worth performing.
- Spell it, in four words. For each word, deal one card off the top into a pile on the table for every letter, then drop whatever is left in your hand on top of that pile and pick the nine up again. The words are the value, then OF, then the suit, then MAGIC.
- The fifth card you deal on M-A-G-I-C is theirs. Do not drop the rest on top that last time — turn the card you land on.
The only two things that can go wrong
Their pile went somewhere other than on top, or you dropped the remaining cards underneath the dealt pile instead of on top of it. Both give you a card that is not theirs and no way back. Everything else — which nine cards, which pile they point at, what their card happens to be — cannot hurt you.
Why does the nine card trick work?
Because of one rule about dealing, and it is worth stating on its own before anything else, because everything on this page falls out of it.
Deal k cards off the top one at a time, then drop the rest of the packet on top of them. A card sitting at position p ends up at position 10 − p — provided p is no bigger than k. And the answer does not mention k.
That last part is the whole thing. Dealing four cards and dealing eight cards do something completely different to the packet, and yet they do the same thing to a card near the top. So a spelling can be any length it likes and the card does not care.
Why 10 − p: dealing one at a time reverses the cards you deal, so the card that was pth from the top of the hand ends up pth from the bottom of the dealt pile. Drop the rest on top and the pile is nine cards again, so pth from the bottom is 10 − p from the top.
Following their card through the four words
| You spell | Letters | Because | Their card |
|---|---|---|---|
| — | — | their pile went on top | 3rd |
| the value | 3 to 5 | 3 ≤ letters, so 10 − 3 | 7th |
| OF | 2 | 7 > 2, so it just moves up two | 5th |
| the suit | 5 to 8 | 5 ≤ letters, so 10 − 5 | 5th |
| MAGIC | 5 | the 5th card dealt | theirs |
The two coincidences it rests on
The shortest value is three letters. ACE, TWO, SIX, and TEN. That is exactly why their card starts third: any shorter and the rule would not apply to it, and a four-letter floor would let it start fourth instead.
Which makes the Ten the one to watch. It is spelled T-E-N, and the card in their hand prints a numeral. Somebody who deals two cards for "10" is a letter short of the minimum the whole trick is built to, and it misses. Say it out loud when you hand the packet over: spell it the way you would say it.
The shortest suit is five letters. CLUBS. Their card arrives at the suit sitting fifth, and 10 − 5 is 5, so the suit spelling puts it back where it already was. That is why the suit can be CLUBS or DIAMONDS, five letters or eight, and the trick does not notice.
Then MAGIC is five letters, and their card is fifth. It is not a coincidence that the word has five letters; it is the word that was chosen because the card is there.
Why does the nine card trick use nine cards?
Because nine is the only number that works. Not the neatest one — the only one.
Below is every packet size from four to twenty, each one run through with all fifty-two card names in your browser. Two columns matter. Lands on asks whether the card reaches one predictable position at all. Any word finds it asks the harder question: whether that position is a fixed point, so a word of any reasonable length lands on it, rather than a number the performer has to count to exactly.
Every packet size, run through
Eight is the near miss. It does land the card somewhere predictable — fourth — but four is not a fixed point in a packet of eight, so the performer has to stop and deal exactly four. MAGIC, at five letters, sails straight past it. Nine is the only size where the card sits still.
The two constraints are the two suit names, pinching from either side:
- CLUBS is five letters, the shortest. For all four suits to give the same answer, that spelling has to reverse the card rather than lift it, which needs the card at position five or less. So the middle is at most five, and the packet is at most nine.
- DIAMONDS is eight letters, the longest. You cannot deal eight cards from a packet of seven, so the packet is at least eight.
A packet needs an odd size to have a middle at all. Odd, at least eight, and at most nine leaves exactly one number, and it is not a number anybody chose.
Questions people ask
What is the card trick with 9 cards?
Nine cards go into three piles of three. Somebody picks a pile and remembers its bottom card, and that pile is dropped on top of the other two. You spell their card out of the packet — value, OF, suit, MAGIC — dealing one card per letter and dropping the rest of the packet on top after each word. The fifth card on MAGIC is theirs.
Where does their card have to be for the nine card trick to work?
Third from the top. That is the only position that works, and it works for every one of the fifty-two card names. Dropping their pile of three on top of the other six puts the bottom card of it exactly there, which is why that step is the one to get right.
Why does the nine card trick work for every card name?
Because of one rule about dealing, and it is set out in full above: deal k cards and drop the rest on top, and a card at position p lands at 10 − p whenever p is no bigger than k. Every value is at least three letters and every suit at least five, which is all the rule needs.
Does it work with a different number of cards?
No, and that is stronger than it sounds. Run every packet size through the routine and only two land the card anywhere predictable: eight and nine. Eight puts it fourth, but fourth is not a fixed point there, so the performer has to count to exactly four and MAGIC misses. Nine is the only size where the card sits still, and the table above deals out every size so you can see it.
The rule is 10 − p because the packet is nine. Change the packet to n and it becomes n + 1 − p, so the arithmetic survives but the landing position moves out from under the words.
Do you need to set up the deck for the nine card trick?
No. Any nine cards from any deck, shuffled by anybody. Nothing in the method depends on which nine they are.
Why is it called a problem?
Because Jim Steinmeyer published it as one. The trick is easy; showing that it cannot fail for any of the fifty-two names is the part worth doing, and it is above.
More
The 21 card trick narrows a packet the same way, by dealing rather than by spelling. Count to 13 is the other one where two quantities cancel and you can watch them go. The rest are on the card tricks page, and the ones with a proof behind them are under mathematical card tricks.
Harrison Alley
Hobbyist · Writes Sleightless
A hobbyist, not a professional. I write up the self-working end of card magic, because it is the door I would point a beginner at, and every trainer here is played through and checked before it ships.