Arrange cards with values ace through 9 in a row, in counting order, with the ace on the left.
Take up a card from one end of the row — left or right, your choice.
Do this twice more, each time taking up either the leftmost or the rightmost card in the remaining row.
Now you have three cards. Add their values, divide the total by six, and call the result n.
Consider the order of the cards that remain on the table.

The card in the nth position (counting from left to right) will be the 4.

Please explain why.

(In reply to Solution and a follow-up by Jer)

The word author is not the right word in this case, it is a well known

self-producing trick.

Re your remark, - any generalization is always welcome!

Posted by Ady TZIDON on 2015-11-02 14:23:31