How Does This Work Then?

[Andy Moore]

http://break.com/index/pick_a_number.html

[Nos4r2]

It didn't work for me-it got it wrong. Honest

It's based on a fairly simple mathematical progression actually, but as I'm feeling fairly simple in all this heat I can't think how to put it in writing

[Poly]

Any two digit number minus the sum of the two digits always gives an answer which is a multiple of 9. i.e. 9,18,27,...81

The table at the end has the same symbol for each of these numbers (9...81) and so it will always predict the correct symbol. To make it seem cleverer it randomises which symbol it uses each time you "play the game" so that you don't spot the pattern so easily.

The mathematical "proof" is that if you pick two digits a and b. Then the two digit number is 10a+b. If we call your answer q

10a + b - (a + b) = q
10a + b - a - b = q
9a = q

therefore q must be a multiple of 9.

[Nasher]

Originally Posted by Polwart

The mathematical "proof" is that if you pick two digits a and b. Then the two digit number is 10a+b. If we call your answer q

10a + b - (a + b) = q
10a + b - a - b = q
9a = q

therefore q must be a multiple of 9.

So how does this work then?
Its too hot and its after midnight.

Nasher.

[Andy Moore]

Originally Posted by Polwart

To make it seem cleverer it randomises which symbol it uses each time you "play the game" so that you don't spot the pattern so easily.

Ah, that's the cunning bit!

[Poly]

Originally Posted by Nasher

So how does this work then?
Its too hot and its after midnight.

Nasher.

Nasher - i'm not sure if you are winding me up - but I am avoiding work so I will answer you!

The instructions are: pick a two digit number, (for the sake of argument I will use 29 to illustrate my explanation, but it will work with any two digit number (that doesn't start with a zero!)). {in my mathematical "proof" above the first digit (a) is 2, and the second digit (b) is 9. So our two digit number is 10a+b = 29}

The instructions then say to add the two digits together (in our example that is 2+9=11) and subtract them from the original number. This is the number you have to look up the symbol for in their table. {in general terms this means we have to add a+b and subtract it from 10a+b}

In our example that gives us 29-11 = 18.

{In the mathematical proof that gives us our solution (which I called q) = 10a + b - (a+b), which when you rearrange the algebra gives q = 9a, and since a in an integer (it is the first digit of your two digit number) then 9a must be a multiple of 9}

If you look at the table - it "randomises" the symbols it allocates to each number so each time you play you seem to get a different number BUT 9,18,27,36,45,54,63,72,81 always have the mathcing symbols in each randomly generated table.

EDIT { actually this will work with a number starting with a zero - the answer, q, will be zero though and its not in the table they provide }