27 Jan '15 22:521 edit

Guys and girls in this forum that know more than me in number theory please help me out on this since it is driving me crazy.

I received this simple problem via whatsapp (I'm paraphrasing):

Follow the instructions below to see what of these movies is more related to you:

think of a number between 1 and 9

Multiply it by 3

Sum 3 to the result

Multiply the result by 3

Edit: Add the final digits and check your movie!

1 - Matrix

2 - My big fat wedding

...

9 . The pleasure of taking it in the a$$

...

18 - Rambo

I thought of 3 and got 9. Well I obviously wouldn't tell people what I've got so I tried again with 2 and also got 9. Hmmmmm... What's going in here?! Let me try 6... It is also 9!!! Gasp! adam's warlock conjecture: The result is always 9 regardless of the initial value one chooses.

Let me write in full the steps we are given:

x is the original value. Then by following the instructions it is

3*(3x+3)

Which is

9*(x+1)

Well this is just the multiplication table of 9 which can be written like this. The right most digits are

9

8

7

6

5

4

3

2

1

0

and the left most digits are

0

1

2

3

4

5

6

7

8

9

Putting the left most and right most digits together it is

09

18

27

36

45

54

63

72

81

90

which "explains" why the sum must be 9.

Well of course this doesn't explain anything at all since the "rule" that we used to write the multiplication table of 9 is what needs explanation in the first place.

So I can see that the result of summing the digits is 9 because one of the factors is 9 and we are using the decimal base as our number system (if the expression is 4*(x+1) and you are using base 5 the sum of the digits will always be 4 and you can proceed analogously from there) but I can't prove it in a rigorous way...

:'(:'(:'(

Can someone just give me hint on how to do it?

I received this simple problem via whatsapp (I'm paraphrasing):

Follow the instructions below to see what of these movies is more related to you:

think of a number between 1 and 9

Multiply it by 3

Sum 3 to the result

Multiply the result by 3

Edit: Add the final digits and check your movie!

1 - Matrix

2 - My big fat wedding

...

9 . The pleasure of taking it in the a$$

...

18 - Rambo

I thought of 3 and got 9. Well I obviously wouldn't tell people what I've got so I tried again with 2 and also got 9. Hmmmmm... What's going in here?! Let me try 6... It is also 9!!! Gasp! adam's warlock conjecture: The result is always 9 regardless of the initial value one chooses.

Let me write in full the steps we are given:

x is the original value. Then by following the instructions it is

3*(3x+3)

Which is

9*(x+1)

Well this is just the multiplication table of 9 which can be written like this. The right most digits are

9

8

7

6

5

4

3

2

1

0

and the left most digits are

0

1

2

3

4

5

6

7

8

9

Putting the left most and right most digits together it is

09

18

27

36

45

54

63

72

81

90

which "explains" why the sum must be 9.

Well of course this doesn't explain anything at all since the "rule" that we used to write the multiplication table of 9 is what needs explanation in the first place.

So I can see that the result of summing the digits is 9 because one of the factors is 9 and we are using the decimal base as our number system (if the expression is 4*(x+1) and you are using base 5 the sum of the digits will always be 4 and you can proceed analogously from there) but I can't prove it in a rigorous way...

:'(:'(:'(

Can someone just give me hint on how to do it?