Magic Square Cube 2x2

[MagicNRS]

Someone showed me a card trick with a regular shuffled card deck (52 cards) and a 2x2 cube.
The video can be found here https://bit.ly/3xKmPPa ( GDrive mp4 file ).
So, each square has 2x2 = 4 tiles, since its a cube there are 6x4 = 24 tiles. Each tile has a low number.
Spectators shuffle the deck and twist the cube.
When they are satisfied the performer asks a spectator to count the sum on top of the cube, which is 16.
Then they count of to the 16th card and he says, that would have been card X...
However, we are going to use the bottom of the cube which is unknown to all of us.
The sum of those tiles equals 12. After counting another 12 cards down it turns out to be the 6 of clubs.
This exactly matches the forecast which was on the table from the start.
HOW DOES THIS WORK: How to construct such a cube?
Some assumptions/remarkable notes
The difference between 16 and 12 = 4,
Each square has 4 tiles with low figures,
6 squares x 4 tiles = 24,
Does it work like a magic square, how is it constructed, what is the formula/the math?

 

[Cubist]

Rubik cubes are very interesting.

The three stickers adjacent to a corner are always fixed next to each other (because the 8 corners are themselves solid chunks of plastic/ wood/ whatever material - like 8 smaller cubes on the corners).

And you can't have just one corner rotated the wrong way (unless you've peeled the stickers off and put them back on the wrong way). If one corner is incorrectly rotated then you can guarantee that at least two others will be incorrect too. Perhaps this cube relies on some interesting fact about this property.

We'd have to study the actual cube to be sure. And actually if I knew the secret then I wouldn't want to divulge it.

Obviously there's some trickery going on with the deck of cards too. Something like forcing a known card into a certain position of the deck. I just know that I'd never play cards, for money, with someone who can spread the pack so evenly and effortlessly across the table like he did A nice trick.

 

[MagicNRS]

Thanks for your reply. Still the question remains: how to construct such a cube mathematically/what formula to use?
A deck of cards always is 52 cards (fixed value variable).

 

[Cubist]

Cubist's Cube

I've designed my own magic 2x2x2 cube. I believe this is a better design than the one in the video because the numbers look more jumbled up. However, it requires (slightly) more arithmetic skill to perform the trick.

If you want to make one, at your own risk, then put some easy to peel-off stickers on your own 2x2x2 cube and then write the following numbers on them...

    9 1
    4 3
7 6 5 2 1 3 2 8
9 2 3 6 7 4 5 8
    4 5
    7 6

NOTE: Use something that peels off easily and won't leave a horrible tacky feel because you wouldn't want to ruin your cube!

Write the numbers 6 and 9 with an underline. If you only have a standard 3x3x3 Rubik cube then you can put stickers on the corner pieces (since the corners of a 3x3x3 behave exactly like the corners of a 2x2x2 - just leave the middle and edge pieces without stickers)

I think you'll be able to work out for yourselves how to determine the sum of the numbers on the hidden side. If you can't then here's a hint...

Spoiler: cryptic hint

What has the number 39 got to do with this trick?

 

[Steven G]

The numbers must be placed on the cube in a way that you can figure out the sum of the numbers on the bottom side. I have no idea how this guy gets the card he wants in that position number since I watch part of that video a few times and he does not touch the cards after the cube is mixed. I also noticed that the sum of all sides do not have the same sum. One way of doing this is to put the desired card in a few places--namely in the positions of all possible face-sums. The problem is that he initially counted down the cards that matched the top sum and it did NOT match the hidden card. I'm baffled.

 

[Cubist]

The numbers must be placed on the cube in a way that you can figure out the sum of the numbers on the bottom side. I have no idea how this guy gets the card he wants in that position number since I watch part of that video a few times and he does not touch the cards after the cube is mixed. I also noticed that the sum of all sides do not have the same sum. One way of doing this is to put the desired card in a few places--namely in the positions of all possible face-sums. The problem is that he initially counted down the cards that matched the top sum and it did NOT match the hidden card. I'm baffled.

I'll send you a private message to let you know how I think it's done. If any other helper wants to know then message me (I think it would be wrong to reveal this to lots of people)

 

[MagicNRS]

I'll send you a private message to let you know how I think it's done. If any other helper wants to know then message me (I think it would be wrong to reveal this to lots of people)

Please drop me a private message, appreciated!

 

[Cubist]

Please drop me a private message, appreciated!

I'm sorry, but my moral compass stops me from revealing more of my thoughts about this trick to someone I don't know. The magician probably invested a lot of time and effort to invent this idea. I don't know what you'd do with the answer (you may have an internet following to whom you reveal magic tricks). I know that Steven G, and the other helpers, would only have a personal interest in the math side.

Anyway, there's a massive clue (about my suspicions) in post#4. That's a genuine post and not a joke. The grinning face is only there because I amused myself with the name "Cubist's cube". It's possible to work out my thoughts, without even applying stickers, because the answer can be determined with:- the cube numbers (in post#4); the spoiler; some time and a small amount of arithmetic.