How to perform extraordinary feats of mental skill

Everyone knows Rain Man, the 1988 film telling the story of an autistic savant, wonderfully played by Dustin Hoffman. The character Raymond was modelled on was the autistic “mega savant” Kim Peek, who displayed mind blowing feats of mental skill. You can search for him on YouTube and watch him perform — it is quite extraordinary.

Except I am not convinced that all of it is true. Kim, who has mental and neurophysiological problems, is clearly not autistic. His memory is remarkable, and he can recite large passages of Shakespeare, memorize the data of cities and highways, and many other such feats. In the wake of Rain Man he became a celebrity and under the supervision of his father performed on stage and film for an enraptured audience.

Some claims made for Kim Peek are quite outlandish. It is said he reads books two pages at a time, scanning each page separately with one eye. That, any neuroscientist will tell you, is not how the brain — any human brain — can process optical information from the eyes. This improbable ability is always described, but never rigorously tested, which would be fairly simple.

But it is some of the demonstrated mental feats performed by Kim Peek that are unconvincing. Again and again and again he is asked to name the weekday of a date, usually a birthday, in the past. And when he does this correctly, the audience gasps in amazement. Many years ago I decided to duplicate this feat. The math behind it is as follows:

  1. Take the last two digits of the year you are given and divide it by 4, discarding any fraction left over;
  2. Add the day of the month.
  3. Add a key value for the month: JFM AMJ JAS OND = 144 025 036 146
  4. Subtract 1 for January or February of a leap year.
  5. Add the last two digits of the year.
  6. Divide by 7 and take the remainder, which tells you the day of the week (Sunday=1, Monday=2, etc.)

Take an example: say your friend tells you he was born on August 2nd 1960. You first divide 60 by 4 (=15); add 2 for the day of the month (=17); add 3, the month’s key value, (=20); add 60 (=80), and divide by 7 (=11, remainder 3). So the final result is 3, and that translates to Tuesday — as this Weekday calculator will confirm. You can use it to practice.

It took me about ten minutes to learn the above algorithm, and I estimate it would take me a few days of practice to become a real Kim-like virtuoso at performing the calculations in my mind. But what would I do with this completely superfluous skill? Apart from entertaining people at parties?

If that is what I wanted, there are many other ways of simulating mega savant skills. Let me give you one you can use to impress people no end. I have it from my friend and mentor Christian Hesse, a mathematician with a wry sense of humour.

The amazing card memorizing trick

This is what you do: you take a regular deck of cards, ask your audience to check it, and then remove and conceal a single card. Tell them it must not be a picture card, i.e. not a king, queen or jack (unless you are a professional and can work in modulo 13 — see below). Any other card.

Now someone starts dealing the remaining cards, rapidly, one at a time, face up, into a pile on the table. You will be watching carefully, pressing two fingers on each temple (for effect), and when it is over you reliably name the missing card. The conclusion is clear: you have tracked the 51 cards that were dealt into the pile, and know that the eight of spades, for example, was not amongst them. Challenge anyone to do the same.

The technique you use is as follows:

  1. The cards have face values: ace is one, the other cards are 2, 3, 4, etc.
  2. When the cards are shown you add them together, modulo ten! This means that when you cross ten you subtract ten: for example 4+9=13. You count that as 3. With a little practice this is quite easy. If the card is a picture card you simply ignore it.
  3. Now the total sum of all cards in the deck is 4 x (1+2+3…+10) =4 x 55 = 220. So when all the cards have been dealt the missing amount tells you the value of the concealed card. If you have finished adding all the cards shown and end up with 3 (this is in reality 213) you know that the concealed card is a 7. If you end with 9, then it is an ace. If the final number is zero it is a ten.

But how can you tell the suit? Here we need a method of tracking the cards, but one that does not distract you from the counting. We do it with our feet! If a card that is dealt is a heart, you slightly raise your left heel, if it is a spade you raise your right heel. If you see a second heart you lower your left heel again, and the same with spades: if a second spade occurs you lower your right heel.

What about the other two suits? If a diamond is dealt you simply “reverse” heels: that mean if left is up and right is down you switch to left down and right up. If both are down you raise both, if both are up you lower both. Leaves clubs: here you do nothing with your heels.

When all cards have been dealt there are four possibilities: if only the left heel is raised the card is a heart, if the right heel is raised it is a spade, if both are raised it is a diamond, and if none is raised it is a club. The mathematically inclined can work out why.

In any case you can dramatically announce the suit and number of the missing card. Say you finish with a 2 and only the right heel raised, it is an eight of spades. To make the whole thing into a scam you can look at the ceiling, eyes darting, and pretend you are recalling all the cards that were dealt. If you are really devious you can mutter: “Seven of hearts? No, I saw that. Three of clubs? Saw it.” After half a minute you announce: “the eight of spades is missing!”

And lean back to enjoy the amazement and applause of your audience.

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