Thanks to Patrick Honner and the inimitable Card Mulcahy for pointing me to the origins of this trick. It’s the Fitch Cheney 5-Card Trick.
I was eight, maybe nine, at the kitchen table with my dad. He was describing a professor who claimed his grad student is psychic.
“The professor asks you to draw five cards from the deck,” my dad explained. “Then the professor shows four of them to his grad student, who guesses the fifth one.” My dad paused for emphasis. “He gets it right every time.”
“But he’s not really psychic,” I said. “Maybe he’s whispering it quietly.”
“Could be,” my dad said. “But maybe he doesn’t need to. Maybe the four cards work as a code, telling you the fifth.”
“But the professor doesn’t get to pick the cards,” I said.
“He does put them in order,” my dad said. “And maybe that’s enough. Maybe, given five cards, you can always sequence four of them into a code for the fifth.”
We grabbed a deck of cards from the cupboard and began working through the puzzle aloud. “We’ve got five arbitrary cards,” my dad said. “Four we’ll reveal, and one will remain hidden. First, we need to pick the hidden one wisely.”
“Which should we pick?” I said.
“Well, there are four suits in the deck—spades, hearts, diamonds, and clubs. So with five cards, there’s no way for them all to be from different suits. Among the five, you’re guaranteed to have at least two cards of the same suit.”
“Why does that help, to have two cards of the same suit?” I asked.
“Because,” he said. “We pick one of them to be the hidden card, and the other one we always sequence first.”
“Why?”
“That way, the first card in the sequence always spells out the suit of the hidden card. It’s our indicator card.”
“Okay,” I said. “But how do we know what number the hidden card is? It could be the 2, the Jack, the King, the 7, the 5…”
“Hmm.” My dad furrowed his brow. “Well, there are thirteen possible values: Ace, the numbers 2 through 10, Jack, Queen, and King. We can put them in a circle, like a clock.” He drew a picture:
“Then,” he continued, “the largest possible distance between a pair of cards is six steps.”
I nodded. “But how does that help us?”
“We’ll agree in advance to always take our steps clockwise,” he said. “It’s important that we agree on the direction in advance.”
“Okay,” I said.
“Now, I think of the indicator card as the starting point, and the hidden card as the endpoint. So I just need to communicate the message of how many steps to go—anywhere from 1 to 6.”
“But what about Ace to 8?” I asked. “That’s seven steps.”
“True,” my dad said. “So I would have to pick 8 as the indicator card, and Ace as the hidden card. That way, it’s still just six steps.”
“Hmm,” I said. “But how do you convey the number of steps? You’ve only got three cards left to send the message.”
“Luckily, there are exactly six ways to order three cards. If we label them ‘small,’ ‘medium,’ and ‘big,’ then I can put them in the following orders:
“You can even think of these as three-digit numbers,” he added. “The smallest possible three-digit number means, ‘add one,’ the largest means ‘add six,’ and the others have meanings in between.”
“But what if the sequence has two cards with the same value?” I asked. “Like two Jacks?”
“Then we’ll need to use the suits to distinguish,” my dad replied. “We’ll agree that Spades are highest, Hearts next, then Diamonds, and last are Clubs.”
“Hmm,” I said. This was a little much for me.
“We’ll practice,” my dad said. He picked five cards, quickly concealed one, and laid out the other four in careful order.
“Well, the hidden one is a diamond,” I said.
“Good. And what’s the number?”
“It’s…” I paused. “It’s Jack, plus one. So it’s the Queen of Diamonds.”
My dad flipped over the card. And so it was.
We practiced more. I looked at this spread of cards:
“It’s a spade. Plus six steps, so… the 8 of Spades,” I said. My dad grinned.
I looked at this foursome:
“5 of Hearts,” I declared.
“Focus your psychic powers,” my dad advised, and I saw my mistake.
“4 of Hearts,” I hastily corrected.
“Good work, my psychic son,” he smiled.
It became our little party trick. And now, with this post, I’m busting our illusion open. We had a good run. I hope you enjoy it as much as we did.
