EPTNow let me start this blog off by saying that Arthur Benjamin is very good at math. However, as a performer, he does over exaggerate the difficulty of his tricks. The purpose of this post is to demystify a lot of the stuff that this man does.
1. Squaring 2 digit numbers
While many people believe that Mr. Benjamin has simply memorized the first 100 squares, this is not entirely true. It is likely that instead, he has memorized the first 50 (still impressive, but more doable). After he does this, he can figure out the other 50 by the equation (50+x)^2=2500+100x+x^2. He can sub in any value for x, and since he has the first 50 memorized, he can do all the way to 100.
2. Squaring larger numbers and general multiplication
Now of course, Mr. Benjamin is very fast at single digit multiplication just like any mathematician, but his secret is how he can remember numbers. He partly describes this to the audience at the end of his act when he explains how he can store numbers as words and retrieve them later. Here is how he does it more specifically though. There are many methods to this, but this is what most people use:
0=s, z (z is the first letter of zero)
1=d, t (have one downstroke)
2=n (n has two downstrokes)
3=m (m has three downstrokes)
4=r (last letter of four)
5=l (L is the Roman Numeral for 50 (don't get this confused with 1 because it has a downstroke!)
6=j, g (g is almost a 6 flipped over)
7=k (capital K looks like two sevens)
8=f, v (I honestly don't know why. It was probably just a left over sound. Some people say a cursive f looks like an 8, but I think that's bs)
9=b, p (p is a mirror-image 9. b sounds similar and resembles a 9 rolled around (don't count d, because this has a different sound!))
Therefore, cookie fission is 77802. Careful! It's phonemes, not letters, so double letters still count as one number
3. Finding the missing digit
This is perhaps the most mysterious part of Arthur Benjamin's act, and also the easiest once you learn the secret. This trick is actually conditional. He will only do the trick if an audience member picks a multiple of 3. Once they do, it's square will be a multiple of 9. He acts like he arbitrarily picked a 4 digit number, but it was very deliberate. No matter what they multiply the multiple of 9 by, it will end up being a multiple of 9. Thus, he simply adds up the digits and finds which digit makes it add of a multiple of 9. Voila! All of you can do this, it's simple addition!
4. Day of the week calculator
Someone already wrote a guide on this: http://www.teamliquid.net/forum/viewmessage.php?topic_id=131637
However, I have a different method that I feel is easier:
1. Take the last two digits of the year
2. If odd, add 11, if even, skip this step
3. Divide by 2
4. If odd, add 11, if even, skip this step
5. Subtract from the next largest multiple of 7 (for example, 45 becomes 4 because the next highest multiple of 7 is 49)
6. Add to the century value (Century values: 18__ is 5 19__ is 3 20__ is 2 21__ is 0. It is cyclic and repeats 5, 3, 2, 0, 5, etc.)
7. Take this value mod 7 and find the corresponding day of the week. (Careful! mod 7 will give you a scale 0-6 not 1-7. So monday is 1 not 2)
8. The following dates of the year you are working with will be the day you just found: 4/4 6/6 8/8 10/10 12/12 5/9 9/5/ 7/11 11/7. These are all easy to remember. Also, there is March 0th which will be on the same day (March 0th is my way of expressing February 29/28 depending on if it's a leap year or not). Also, January 3rd/4th will be depending on whether it's a leap year or not.
9. Simply count forward or backward from one of the days listed above to find the day of the week. I could do this in about 15 seconds after about an hour of practice and I'm by no means a math genius. You start recognizing patterns as you do it more which allows you to do it faster.
A trick that Arthur Benjamin does to make it seem like he's doing it faster is he asks for the year first so that by the time they finish telling him the date, he's already done the difficult part. Also keep in mind, that in 1757 (I think...might have been 1759) the British randomly eliminated 11 days from the calender and so this method doesn't work before that year.
Well there ya go! now you can impress your friends with your mathemagic skills too! Also, it's fun to re watch the ted talk once you're in the know.
EDIT: Clarified section 2 a little more
EDIT 2: If anyone is interested my method of the day of the week calculator is called the doomsday algorithm and the system for memorizing numbers is called the major system
