# Emory Valley

## Center for Magic and Math

This is one of those shiny new buildings that pops up - one where we'll take a look at some of the odder bits of 'magic' or 'psychic' tricks that crop up over and over. It's not entirely accurately named - the third trick here (the card trick) isn't math. (But it isn't magic, either.) And I'm nothing like a math whiz, trust me. Still - I remember an episode of Remember WENN where the stage magician said, "People keep saying 'There really is magic', and I just smile and think 'There really is math!'"

So, take a look at some of these and try to figure them out - bearing in mind that you can figure them out. There's no magic or mind reading going on. Here's one making the rounds:

This is pretty neat.
DON'T CHEAT BY SCROLLING DOWN FIRST! It takes less than a minute. Work this out as you read ... Be sure you don't read the bottom until you've worked it out! This is not one of those waste of time things, it's fun.
1. First of all, pick the number of times a week that you would like to have chocolate (more than once but less than 10)
2. Multiply this number by 2 (just to be bold)
4. Multiply the new number by 50 -- I'll wait while you get the calculator.
6. Now subtract the four digit year that you were born.
Now, you should have a three digit number.
The first digit of this was your original number (i.e., how many times you want to have chocolate each week).
The next two numbers are YOUR AGE! (Oh YES, it is!!!!!)
Wow!

Wow, indeed - math is great. By the way, it'll work with 0, but it'll be obvious; and it'll work with 1, so I don't know why they bother to say "more than once"; and it'll work more than 9, except that at the end you'd have a four digit number, not three - the first two digits will be your number. In fact, as long as your age is not over 99, it'll work.

Some varieties of this meme add "This is the only year this will work!" but it's been around several years now. All you have to do is change 1757 to 1758 and it'll work next year, too.

So, how does it work?

Remember the old Tom Lehrer song, "New Math"? "And you know why four plus minus one Plus ten is fourteen minus one? 'Cause addition is commutative, right." That's the key.

Look at this as two different operations. Not as ((n*2) + 5) * 50, they want you to, but as ((n * 2) * 50) + (5 * 50) ... or, because multiplication is commutative, too, as (n * 100) + (5 * 50).

So you have a constant of 250, regardless of your number (n), which will be added to the other constant, 1756, and you have n * 100.

To break it down, then:

In step 2 you multiply your number (n) by 2, and then in step 4 you mulitply 2n by 50 (we'll deal with the 5 in a minute). This means you're multiplying n by 2 and then by 50, which is to say, by 100. Therefore, your number is now in the 1st place of any three digit number, and the second places are zeroes, so they won't affect any adding you do.

Next, back to the 5. You multiply it by 50, too, which gives you 250. That's a constant - no matter what n is, you will have 250 as well as n*100. So when you add 1757 to your result you're adding it to 250 and n*100. (Remember that the 0's don't affect the adding.) So for the moment ignore your n00 and look at the other sum: 250 + 1757.

That's 2007. (And that's why with n=0 it would be obvious. 000 + 1757 + 250 = 2007)

Hey - that's this year. So when you subtract your birthyear from your result (which is 2007 + n00) you will, of course, have your age, plus n00. The zeroes in n00 will not affect your age - you'll have a three-digit number of n and your age.

The only glitch would be if you were 100 or more. Then your three-digit number would start with your n+1, and the last two digits would be the last two of your age (e.g., if you're 103 and picked 6, your number will be 703). So don't send this to any centenarians!

Wow!

Magic? No - just math. It's set up so that no matter what number you choose, its individual digits will always add to 9. So it's trivially easy to come up with one of them when provided with the others.

If you have, say, a three in the number (say 1234), then when you put the 3 in a different place to get your second number, and subtract, then you always get some number which is divided by 9. (or is 0).

For instance - 3000 - 3000 = 0. 3000 - 300 = 2700. 3000 - 30 = 2970. 3000 - 3 = 2997. Notice all the digits add to 9.

So no matter how you scramble the numbers, you end up with an answer where the digits will add to 9, which means that's all the computer has to solve for: your digits that you give it subtracted from 9 equals the digit you chose.

So, if you take 1234 and change it to 4321, your subtractions are:

4000 - 4 = 3996 ( adds to 9)
300 - 30 = 270 (adds to 9)
200 - 200 = 0
1 - 1000 = 999 (negative, but for the trick to work, that doesn't matter)
The real answer would be 3087 = 3 + 8 + 7 = 18 = 1 + 8 = 9

No matter which number you keep back, it's 9 - the other two.

0, 3, 8 = 11 = 2 so the answer is 7
0, 3, 7 = 10 = 1, so the answer is 8
0, 7, 8 = 15 = 6, so the answer is 3
And you're not allowed to save the 0, which would make it not work. (eg, 3, 7, 8 = 18 = 9, so is the missing number 0 or 9?)

If you scramble it to 2143, your subtractions are:

2000 - 200 = 1800 (adds to 9)
100 - 1000 = 900 (negative, adds to 9)
40 - 4 = 36 (adds to 9)
3 - 30 = 27 (negative, adds to 9)
So... 2143 - 1234 = 909 (1800 - 900 + 36 - 27) = 9 + 0 + 9 = 18 = 1 + 8 = 9

and so on. It always works.

I think that's kind of cool.

This one's all over the web. Here's one version:
Card Trick
This one's not math. It's easier than that. Go back, and this time choose two cards. I'll wait.

Notice that although they only took away one card, your other card wasn't there either? That's because all the cards are different. So no matter which card you pick, it'll be gone.

Kind of cheating, this one...

Check out this site: Mind Reading Site Hmmm... it might be gone. That's okay. Here's the instructions: First, choose any two-digit number. Any one at all. Now, add the digits together and subtract the result from the first number. (E.g., you choose 98, 9+8=17, 98-17=81) Find your new number on the chart and concentrate on the symbol. Concentrate real hard. Now ... click here. Wow! How'd I do that??? Well - it's nearly the same as the one above - except that since the numbers will always add to 9, and there are only two digits, it's easy to make sure all the multiples of 9 ( those that aren't too large - you can't get 90 or 99; think about it) have the same symbol on the chart. So that one's even easier to set up.

This one always works. But it's not math. First, check it out. Can you guess?

It's pretty simple. On the first page, when you pick your number, the choices are in a scrambled grid:

 9 21 4 22 7 13 18 11 23 15 8 1 26 5 16 14 24 17 3 2 20 10 12 19 6
You can, of course, ignore all the counting, repeating out loud, and so on. Just pick a number. Then you click on the color of your number. This takes you to the next step. Here you click on a color. This step is completely meaningless. You can click on your number's color, or not. It doesn't matter. It's a distraction, meant to get you thinking about colors. The click takes you to the next page, where the real trick takes place.

Here you're asked to choose the house that has your number in it. Here's the kicker:

House A: 4, 12, 1, 30, 11, 13
House B: 10, 26, 24, 9, 21, 2
House C: 17, 25, 14, 20, 8, 28
House D: 3, 23, 22, 27, 19, 5
House E: 18, 16, 6, 15, 7, 29
See the trick? No? Compare those sets of numbers with the grid.

Each house has one number from each color, plus a number that wasn't even on the grid to start with.

So you see, if you tell the program the color (say, green) and the house (say, C) your number must be 23. It's the only green number in House C.

The "pick a door" step is more razzle-dazzle. The computer (unlike a magician) can put any number it wants wherever you click.

Flashy, but just a trick.

This one almost always works:

* Pick a number from 1 to 10.
* Then multiply that number by 9.
* Take the new number and add the digits together.
* Subtract 5.
* Take your answer and turn it into a letter of the alphabet such as 1=A, 2=B, 3=C, 4=D and so on.
* Pick the name of a country that starts with that letter.
* Take the last letter of the country's name, and think of an animal that starts with that letter.
* Pick a color that starts with the last letter in the animal's name
* Are you thinking of an orange kangaroo?
How's this one work? Well, you should now realize that you've been forced to pick the number 4: any number that's divisible by 9 (and you multiplied by 9 to get your number) will yield 9 when you add its digits up, right? So if you subtract 5 from the result starting with any number, you'll have 4.

That means you've been forced to "D" for your letter. The odds are enormously high that you'll pick Denmark for your country. Very few people will think of Djibouti, Domenica, or the Dominican Republic, which are your other choices.

That means it's likely you'll pick "kangaroo" - not quite as likely as picking "Denmark", perhaps, but pretty likely. And a color that starts with "O"?

The following bit was in Netsurfer Digest some time ago, and is still popular : Well, no. Not really. Although it is admittedly fun. Especially when you start putting in names like Hedy Lamarr (she has a Bacon number of 2, because she was in "The Female Animal" (1957) with Yvonne Peattie, who was in "The Big Picture" (1989) with Kevin Bacon.) But seriously, folks, this kind of thing is prime example of the basic innumeracy that pervades our culture. It's been demonstrated (by Stanley Milgram) that out of the entire population of the United States, the average number of people linking any two randomly selected individuals is 5. The highest number is 10. And here we're looking at only 174,000 people, all of whom are actors. Of course they are connected. There are probably long-time character actors in that data base whose "magic index number" is lower than Kevin Bacon's. 