Photographic Memory: Secret Knowledge
The trick is a flamboyant variation of the one invented by a New Zealand computer scientist called, Tim Bell and also published by CS4FN.
You add an extra row and column of cards to make it seem more complicated but in fact you are setting up the outcome. You are not making things harder, as you suggest, but easier!
What you do is look at the number of blue-facing cards in the first row and if that number is odd, you extend the grid with a new blue-facing card to ensure that the amount of blue-facing cards in that row is even!
If the number of blue-facing cards is even then place the new card as red-facing. You always want an even number of blue-facing cards in every row.
The same procedure applies when adding the extra cards to the columns. Every card you add should create an even number of blue-facing cards. The final card on the bottom right of the last row finishes the set. The set up is complete.
Detecting the Change
Detecting the change doesn’t rely on pattern recognition but your ability to spot the row and column with an odd amount of blue-facing cards. You look at the cards and start from the top, scanning down row by row, looking for blue-facing cards. Remember you added the extra cards to ensure there was an EVEN number of blue-facing cards in each row.
There will now be one row where there is now an ODD number of blue-facing cards: one of the cards in this row was turned over, but which one?
Start to scan the columns now, again looking for the column where there is an ODD number of blue-facing card showing.
When you find it, you’ve found the column with the flipped card!
You now know the row and column position. Like GPS, in a way – you have the longitude and latitude. That is the position of the flipped card is where the row and column intersect.
Can you spot the card that has been turned over?