brainteaser card puzzle

[Eric]

Take one suit from the deck and arrange it so the cards will appear in sequential order when one turns the top card face up, puts the next card on the bottom of the deck, turns the next card face up, puts the next card on the bottom of the deck, and so on.


correct order:

Spoiler: Show

A, Q, 2, 8, 3, J, 4, 9, 5, K, 6, T, 7
[Fooling Some of the People All of the Time pg 20]

[Savy]

woo got it right! Explanation & answer in spoiler.

Spoiler: Show

13 cards

A a 2 b 3 c 4 d 5 e 6 f 7

Because we want every odd card on the original run through to be in order. Then we are left with the cards a b c d e f but this time the first card goes back to the bottom so we want even numbers to be in the order

a 8 c 9 e T

b=8 d=9 f=T

Even cards again as last one was a turn up so the first card goes to the bottom

a J e

c = J

That means we need the next two cards to be in order as the next card is put in the sequence.

a=Q e=K

A Q 2 8 3 J 4 9 5 K 6 T 7

[OngBonga]

A82J394K5T6Q7

[OngBonga]

I can't be bothered to figure out why I'm wrong.

[MadMojoMonkey]

I can't be bothered to figure out why I'm wrong.

Savy's explanation is straight-forward.

[MadMojoMonkey]

a b c d e f g h i j k l m

1st draw

Kept: a c e g i k m
New pile: b d f h j l

Note that m was kept, so the next step is to move from top to bottom.
Let's do that first.

New pile: d f h j l b

Now repeat.
Kept: d h l
New pile: f j b

So now the whole kept pile goes: a c e g i k m d h l
In the last step, b was moved, so the next step is to keep.

Kept: f b
New pile: j

j is final card, moved from top to bottom, which changes nothing, and then drawn as last card.

Final order: a c e g i k m d h l f b j

This is the order the cards will be drawn from an alphabetically ordered set. Just replace this with the desired final order and then rearange back into the alphabetical order.


a c e g i k m d h l f b j
A 2 3 4 5 6 7 8 9 T J Q K

Solution:
A Q 2 8 3 J 4 9 5 K 6 T 7

[OngBonga]

Savy's explanation is straight-forward.

Indeed. After drawing the 7, I forgot the next card goes to the bottom, that's where I went wrong. I just couldn't be arsed to figure that out last night.

[OngBonga]

Note that m was kept, so the next step is to move from top to bottom.
Let's do that first.

New pile: d f h j l b

This is where I fucked up. I didn't move b to the bottom after keeping m. Easy mistake to make on paper.

[MadMojoMonkey]

This is where I fucked up. I didn't move b to the bottom after keeping m. Easy mistake to make on paper.

I made a similar mistake on my first attempt. I moved the f to the bottom during the next step.

[OngBonga]

I arrogantly assumed I'd get it right first time, and when I didn't, didn't care to try again.

[a500lbgorilla]

I arrogantly assumed...

You're the best, Ong

[OngBonga]

And I don't even have to try.

[Eric]

I didn't have a chance to try it because I saw the answer right away in the book (he should have put the answer in the appendix or something).