A handbook of magical mathematical tricks for you to learn
Wow, I’m getting closer to track down your movements. Move along another vector where the numbers add to an odd number. Now I’ll remove more cards I know you’re not thinking of. Finally, move along a vector where the numbers add up to an odd number. After this, using my powers of magic, I think I can say that you are now thinking of the four of clubs. Was I right? Maybe it was magic, or maybe it was maths (or maybe a little of both).
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The reason why this works is a little bit cheeky. To begin with I asked you to think of a card (let’s call the cards in the first picture “set 1”). Notice that to get from your card to any other card in the first picture you always have to move along a vector where the numbers of the vector add up to an even number. If you try to move to the empty spaces (where I put the new cards – call these cards “set 2”) you have to move along a vector where the numbers of the vector add up to an odd number. So when I ask you to move an “even” vector or an “odd” vector, I always know when you’ll be in set 1 or set 2. As I know which set of cards you are on, I can get rid of some of the cards from the other set that you are not in. If I keep doing this there will be less and less cards you can be on until I know your final card, as it is the only card left you can choose. This bit about “odd” and “even” vectors isn’t something you will need for the GCSE exam.