Math trick question

[Petra]

How the bloody hell does this work?

http://www.magictricks.co.uk/mindreader/MagicTricksMR?GXHC_GX_jst=8258c07850ea6165


It's got everyone I know totally beat.


:eh?: :tmcnfusd:

[copiae]

Formidible your mystery may be,
with the answer not easy to see.
Look carefully over the chart to find
The pattern behind whats on your mind.

Look once, look twice, and you may espy,
A link between chart and resultant scry,
Another clue I'll give for free,
The answer lies in a multiple of three.




Sadly, writing that was the most fun I've had all day. Ah well, my break times over :(.

[slimshady2357]

A classic, that one ;)

Here is a hint:

Take a look at the symbols beside the numbers that are divisible by 9 (9, 18, 27, 36,...) you might notice something....

Here is the full reason:

This works because no matter what 2 digit number you choose, if you subtract the sum of the two digits from the two digit number itself, the answer will always be divisible by 9. Check some out and see for yourself....

56 - 11 = 45, 98 - 17 = 81, etc.... and they just make all the symbols beside the numbers divisible by 9 the same symbol. Also, everytime you load the page, the symbol they choose as the 'answer' symbol changes, so you don't catch on ;)

Adam

[Petra]

Formidible your mystery may be,
with the answer not easy to see.
Look carefully over the chart to find
The pattern behind whats on your mind.

Look once, look twice, and you may espy,
A link between chart and resultant scry,
Another clue I'll give for free,
The answer lies in a multiple of three.




Sadly, writing that was the most fun I've had all day. Ah well, my break times over :(.


Rightio, got that.


I think.

[Petra]

A classic, that one ;)

Here is a hint:

Take a look at the symbols beside the numbers that are divisible by 9 (9, 18, 27, 36,...) you might notice something....

Here is the full reason:

This works because no matter what 2 digit number you choose, if you subtract the sum of the two digits from the two digit number itself, the answer will always be divisible by 9. Check some out and see for yourself....

56 - 11 = 45, 98 - 17 = 81, etc.... and they just make all the symbols beside the numbers divisible by 9 the same symbol. Also, everytime you load the page, the symbol they choose as the 'answer' symbol changes, so you don't catch on ;)

Adam


Oh, fuck! Well that threw me !


I need to work on this - I really want to understand the logic...bring it on!!!!

[slimshady2357]

Basically, it all comes down to 10 –1 = 9. Here is why:

You’re taking a two digit number, for instance 58, and then subtracting the sum of the two digits, 13 in our case. This is the same as subtracting 8 and then subtracting 5. If you always think of it this way, as a two step subtraction, you can see better what is going on.

So, in step one, subtract the digit that is the same as the one in the ‘ones’ column of your two digit number. In our case, subtract the 8 from 58. This leaves 50.

NOTE: It will always leave a number divisible by 10, either 10, 20, 30, 40, etc… because you are using the same digit as is in the ‘ones’ column.
So if your number is 43, you subtract 3, getting 40. If it’s 67, you subtract 7, getting 60. See? :)

Then you have to subtract the second digit, which is always the same as the digit in the ‘tens’ column. In our example of 58, we have 50 left and are subtracting 5. If you think about it, this is the same as 10 - 1, done 5 times. And so you will always get an answer that is divisible by 9. This is because your second subtraction will always be something like 50 – 5, or 30 – 3, or 60 – 6, etc… which is always (10 – 1) done a certain number of times.

I hope you can see more clearly why any two digit number minus the sum of the two digits, will always be divisible by 9. After you know that, you can see that the trick becomes quite clear :)

Adam

[JoeP]

Here's another way of seeing why the number you choose is always divisible by 9. ... Using the power of symbols ... which may be clearer or more frightening, I can't tell.

Any two-digit number can be written as a*10 + b, where a and b are numbers (integers) from 0 to 9.

It's easy to write down the sum of the digits:
a+b.

So it's also easy to write down what you get if you subtract the sum of the digits from the number you first thought of:
(a*10 + b) - (a+b)

Calling on the power of algebra, this is the same as:
a*10 - a + b - b

which is the same as:
a*10 - a

which is the same as:
a*9

which is obviously a multiple of 9.

[slimshady2357]

JoeP, I was afraid to use the wonderful power of algebra. I never know if it's going to scare someone off.

But when I read your explanation as compared to mine, I find it to be much more concise and much clearer. :)

Adam

[Clutch Munny]

Both explanations are excellent relative to their aims.

[Petra]

Thanks!

I got it now. :yup: