Assume when you count five cards over behind your back when the five face up cards are further down the packet. Turning those five over results in ten face up cards in each hand.
Now assume one of the face up cards is amongst the five you count across behind your back. Turning this packet over turns four cards face up and the other card face down. The other original face up cards remain face up in the other hand.
The packets have the same number of face up cards, not the same number of cards.

let x = the number of face-up cards in the 5 you take off the top of the deck.
the number of faceup cards in the remaining 15 is 5 – x.
when you flip the 5, the x cards become face down, and the remainder become faceup.
that remainder is 5 – x.

When you take 5 cards off the top, you have taken some face up cards with them; you don’t know how many, but let’s say 2. When you turn this “top stack” over, there are now 5-2, or 3 face up cards in that stack. In the bottom stack you left 5-2, or again, 3 cards facing up.

With a little thought, you can see that it’s true no matter how many up-cards (including zero) were taken in the top stack..

The cute thing about the solution is you have no idea how many cards are going to be face up in each stack when you’re done…only that they’re the same.

There was a Friday puzzle that begins with 100 coins laid on a table with 10 of them heads and the other 90 tails. The trick was to ask a blindfolded participant to arrange the 100 coins into two piles, each containing the same number of heads after the coins had been randomized. The solution involves the same “math”. Randomly turn over ten coins and place them in one pile. The remaining 90 coins constitute the second pile. They will each contain the same number of heads.

Why does the U.K. refer to math as maths? I suppose for the same reason there is a “u” in colour. Just asking.

How does that work?????? Wouldn’t the number of turned-over cards in each lot be random each time? I don’t get that . . .

Assume when you count five cards over behind your back when the five face up cards are further down the packet. Turning those five over results in ten face up cards in each hand.

Now assume one of the face up cards is amongst the five you count across behind your back. Turning this packet over turns four cards face up and the other card face down. The other original face up cards remain face up in the other hand.

The packets have the same number of face up cards, not the same number of cards.

Sorry, the last sentence of that first paragraph should finish:

…. results in ten face up cards, five in each hand.

let x = the number of face-up cards in the 5 you take off the top of the deck.

the number of faceup cards in the remaining 15 is 5 – x.

when you flip the 5, the x cards become face down, and the remainder become faceup.

that remainder is 5 – x.

Excellent material. Something I probably will use in my jext bar visit!

Reblogged this on Oyia Brown.

Simple explanation:

When you take 5 cards off the top, you have taken some face up cards with them; you don’t know how many, but let’s say 2. When you turn this “top stack” over, there are now 5-2, or 3 face up cards in that stack. In the bottom stack you left 5-2, or again, 3 cards facing up.

With a little thought, you can see that it’s true no matter how many up-cards (including zero) were taken in the top stack..

The cute thing about the solution is you have no idea how many cards are going to be face up in each stack when you’re done…only that they’re the same.

Oh yes. Now I see. It’s very logical. Just SEEMS strange! Good one.🙂

I’ve this as a puzzle before – makes a neat card trick

There was a Friday puzzle that begins with 100 coins laid on a table with 10 of them heads and the other 90 tails. The trick was to ask a blindfolded participant to arrange the 100 coins into two piles, each containing the same number of heads after the coins had been randomized. The solution involves the same “math”. Randomly turn over ten coins and place them in one pile. The remaining 90 coins constitute the second pile. They will each contain the same number of heads.

Why does the U.K. refer to math as maths? I suppose for the same reason there is a “u” in colour. Just asking.

One might just as well ask why the U.S. refers to maths as math.