# Can anyone explain how this works?

Discussion in 'Off Topic [BG]' started by Petebass, Feb 9, 2006.

1. ### Petebass

Dec 22, 2002
QLD Australia
2. ### Petebass

Dec 22, 2002
QLD Australia
Never mind - I worked it out. It's still pretty neat huh?

Apr 13, 2001
berkeley, ca
magic.

no, it's actually psychological.

notice that the example they give you has an answer of 18.

notice which symbol corresponds with 18. (it changes each time.)

notice which symbol the crystal ball reveals each time.

man, i should be studying for my abstract algebra exam tomorrow.

i hope it's as easy as this!

Apr 13, 2001
berkeley, ca

d'oh! beat me by a few seconds.

5. ### MikeyFingers

Aug 1, 2005
Long Island, NY
I hate these things. They make me feel stupid. I know there's simple math trick used for it, but I can never figure it out, I suck at math.

6. ### Jazzin'...Bluesin' and Funkin'

There are only so many answers you can get from that equation. All those answers have the same symbol. Its not even psycological.

Apr 13, 2001
berkeley, ca
ah, they say pick ANY two digit number, not 23.

but everyone's going to pick 23.

8. ### Petebass

Dec 22, 2002
QLD Australia
Ditto. What makes it worse is that you KNOW it's mathematical, you KNOW there's no such thing as magic....

Brad only worked it out because was studyig for an algebra test and was already in a maths frame of mind. That's my excuse and I'm sticking to it

Apr 13, 2001
berkeley, ca

10. ### fookgub

Jun 5, 2005
Houston, TX
This one's simple. If you have access to Matlab, try putting this in:

tens = floor([1:.1:9.9]);
digits = [10:99];
ones = repmat([0 1 2 3 4 5 6 7 8 9],1,9);
ones = ones(1,;
result = digits-(tens+ones);
scatter([10:99],result);

From the graph, you'll see the allowable results are 9,18,27,36,45,54,63,72, and 81. Oddly enough, the first 9 multiples of 9. I'm not really sure why it works out that way, but it's interesting. Anyway, look on the histogram and you'll see each of those numbers has the same symbol.

I've seen some neat 'mind readers' using number or card tricks, but this isn't one of them... it's too easy.

I attached the Matlab plot if anyone's interested.

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Apr 13, 2001
berkeley, ca

ah, i didn't catch that!

damn, man. i had to read this right before i went to bed. now i'm going to be bothered by proving how this works out.

quick edit: figured it out (without even using matlab!)

let "i" denote a two digit integer.

i = 10x + y, where x is an integer from 1 to 9 and y an integer from 0 to 9. (x can't be 0, otherwise "i" wouldn't have two digits!)

now consider i - (x + y) = 10x + y - (x + y) = 9x.

hence the first nine multiples of 9.

(i originally thought that the problem would boil down to something like this; i should have taken a second to figure it out!)

12. ### g00eY

Sep 17, 2005
Chicago, IL
i did it wrong the first time, then all the other times i was just like what... the... heck? it scares me.

Apr 13, 2001
berkeley, ca

bah, it's just "mathemagic." there're little books you can buy (at least one of which incorporating the term i put in quotes) full of stuff like this. or see on the internet.

it all comes down to having people do some things that you want them to do, and then have them be amazed.

14. ### Mark WilsonSupporting Member

Jan 12, 2005
Toronto, Ontario
Endorsing Artist: Elixir® Strings
I still don't get it :\

Anyone care to explain to someone who doesn't get math at all?

-Mark

Apr 13, 2001
berkeley, ca
not even after reading what i did?

alright, so a two digit number has a tens digit and a ones digit.

let's look at 42.

we can, if we want, rewrite this in an equivalent manner as so:

4x10 + 2x1.

you multiply the tens digit (4) by ten (not a coincidence!) and the ones digit (2) by one (also not a coincidence!).

so in a more general sense, a two digit number "yz"* can be written as

y x 10 + z x 1. or, if the x's are confusing, 10y + z.

the instructions are to take this number, 10y + z, and subtract the sum of y and z from it.

so (10y + z) - (y + z).

then doing some rearranging, we get:

(10y - y) + (z - z).

that's the same as 9y.

y can be 1, 2, 3, 4, 5, 6, 7, 8, or 9. it can't be zero, otherwise 10y + z would just be z, which is a single digit. likewise, it can't be any more than 9, or else it would have three digits.

so the programmer for that site made sure that the symbols for 9, 18, 27, etc., all were the same, as those are the only possible answers.

*please don't be confused about this; from algebra onwards, we are accustomed to writing this as a multiplication of two numbers y and z. but just kind of forget about that convention for a sec and try to follow me.

16. ### Hambone

Mar 18, 2000
Atlanta/Loganville
Did it twice with different numbers/symbols and it didn't work either time. All I was doing was picking my zodiac sign - scorpio.

There was another of these that displayed 5 face cards. You were to pick one of them and the computer would reshuffle the cards and each time it would remove the card you picked. And it worked every time. How? They would deal a different set of 5 face cards each time so of course yours wasn't there. It worked because while you were concentrating on YOUR card, you weren't paying attention to what the other cards were. Clever, but it took two plays for me to pin it down.

17. ### Vorago(((o)))

Jul 17, 2003
Antwerp, Belgium
damn I feel stupid

18. ### nateoSchubie Fan #1

Mar 2, 2003
Ottawa, Ontario
Algebra has its place, but it can be confusing and this problem doesn't really need it (though it is a nice proof, if you're into that sort of thing). Here's my crack at a repeat explanation with minimal equations.

The way I look at it is this. Basically what you're doing is subtracting the digits from the original number one at a time (you add them together first, then subtract the result). If we take the standard number of 23, then our result is basically 23 - 2 - 3 = 18.

The real trick of it is when you subtract the second digit. Any two digit number you have will boil down to a multiple of ten minus the first digit. For example:
23 - 2 - 3 = 20 - 2
42 - 4 - 2 = 40 - 4
57 - 5 - 7 = 50 - 5

From there it's just a fun quirk of mathmatics that the results are all multiples of 9 (as Brad said, 10x - x = 9x). In the end every two digit number you pick will be a multiple of 9, so simply using the same symbol for multiples of 9 makes the program work every time.

Sorry Hambone, but your math must be off.

-Nate

Apr 13, 2001
berkeley, ca

i don't think you're playing by the rules, hambone!