Same answer for multiplication

[Cazpz]

Hello all, I sometimes do sums in my head to help me sleep and have found a calculation which gives the same answer whatever numbers I use. Please bear with me as I’m no expert.

take any number except one containing a 5 or 0. This is how it goes:

4 x 4 = 16 multiply these two digits
1 x 6 = 6
6 x 6 = 36 and again
3 x 6 = 18
1 x 8 = 8 *
8 x 8 = 64
6 x 4 = 24
2 x 4 = 8 *
The answer will always be 8 whatever number that is used. if a number contains 5 or 0, the answer will always be 0.
If the numbers are added, then the answer is 1.
My question is, is there a name for this rather weird result?
Please ask if I’m not clear enough.
Thanks

 

[Steven G]

You say that The answer will always be 8 whatever number that is used. if a number contains 5 or 0, the answer will always be 0. How can that statement be correct? After all, if the answer is always 8 whatever number you used (you said this, not me), then how can you then say that the answer will always be 0.

In mathematics you have to be precise! You meant to write is, The answer will always be 8 whatever number that is used except if the number contains a 0 or 5. If a number contains 5 or 0, the answer will always be 0


If the numbers are added, then the answer is 1. I really have no idea which numbers you are referring to that sum to 1.

 

[Steven G]

Does the first multiplication have to be with the same number? Does the 1st number have to be a digit? If yes, you really need to state this!

Note that 2*2 = 4, 4*4 = 16, 1*6=6 which is not 8. Of course you can continue with 6*6 = 36, 3*6 = 18 and 1*8=8.

Note that 1*1=1 and you never get 0 or 8.

 

[Steven G]

How's that?

I know people too. I got my post fixed!

 

[Steven G]

You say that The answer will always be 8 whatever number that is used. if a number contains 5 or 0, the answer will always be 0. How can that statement be correct? After all, if the answer is always 8 whatever number you used (you said this, not me), then how can you then say that the answer will always be 0.

In mathematics you have to be precise! You meant to write is, The answer will always be 8 whatever number that is used except if the number contains a 0 or 5. If a number contains 5 or 0, the answer will always be 0


If the numbers are added, then the answer is 1. I really have no idea which numbers you are referring to that sum to 1.

I re-read you post and you clearly said take any number (and multiply it my itself)

 

[Cubist]

Hello all, I sometimes do sums in my head to help me sleep and have found a calculation which gives the same answer whatever numbers I use. Please bear with me as I’m no expert.
...
My question is, is there a name for this rather weird result?

I found this post interesting, even if it isn't completely correct. I've never heard of a name for these specific sequences (click)
Exceptions (if starting with a number between 0 and 99)
0, 0,0, ...
1, 1,1, ...
11, 1, ...
OK, 5 is a digit in the second number of the following exceptions:-
69, 54, 20, 0, ...
78, 56, 30, 0, ...
87, 56, 30, 0, ...
96, 54, 20, 0, ...

If the numbers are added, then the answer is 1. I really have no idea which numbers you are referring to that sum to 1.

Just sum the digits instead of multiplying. All of the starting numbers (from 0 to 99) will end up in one of the following repeating cycles...
0, 0, 0...
1,2,4,8,16,7,14,5,10, 1,2,4,8,16,7,14,5,10, 1...
3,6,12, 3,6,12, 3...
9,18, 9,18, 9...

EDIT: OP, you might be interested in the Collatz conjecture (click) if you're really struggling to sleep

 

[Cazpz]

Does the first multiplication have to be with the same number? Does the 1st number have to be a digit? If yes, you really need to state this!

Note that 2*2 = 4, 4*4 = 16, 1*6=6 which is not 8. Of course you can continue with 6*6 = 36, 3*6 = 18 and 1*8=8.

Note that 1*1=1 and you never get 0 or 8.

Hi Steven, thanks for your reply. You’ll note that I did mention that this answer 8 is always, without exception, the result of choosing any number except those which contain 0 or 5. So leave them out for the moment and try this exercise with ie. 9 or 6 or 7. Do the same calculations I did and see what happens. I’m not saying I’m a mathematical genius by any means. I just thought it was an interesting result and that you lovely folk may have tried it and thought ‘wow, that’s weird’. I’m grateful for any positive response and would rather you phrase your reply in a more kindly fashion.