This is too complicated for you ... I can give you a hint ... 2 1 card will be reduced to 9 cards, just like yours, arranged from left to right ... in three columns ... with three cards in each column. Each column of cards that are dealt later also presses the cards in front. ...

1 2 3

4 5 6

7 8 9

The first step .. Let the player remember which card he thinks of any nine cards. He'd better write the card in the position of 9 ... 9 is in the third column ... and then put the columns where 9 is in order ... that is, 9 presses, 8 presses and 7 presses.

Step 2 .. The first column12 3 is put away. The second column 4 5 6 is also put in order. ..

Step 3 ... put the column where 9 is in the middle of the first column and the second column ... This is the key ... As for the first column and the second column, it doesn't matter which one is above and which one is below ... We will put the first column 1 2 3 in the middle ... and the second column 4 5 6 is at the bottom.

The fourth step ... is also the key ... Just now, the cards were dealt from left to right ... Now this step is to play the cards from top to bottom, and then form such a group.

3 9 6

2 8 5

1 7 4

Then the group of cards that the player remembers will naturally be sent to the middle group. Then ask the player if the cards he thinks are in the left-to-right group. Then there is the middle number of the group he said, which is Example 9. In the middle of the first group.

No matter what cards the player thinks, as long as I deal the cards well, the cards he thinks will be in the middle of his final confirmed group. ...

I'm not very clear about any mathematical theorem. ...