Another math question

[nothing]

x % 10 = 8

How can I know what x is?

[downpour]

I think mod gives you the remainder of division, right? I could be wrong, but I think I'm right. So...

x % 10 = 8 means x could be anything divisible by 10 that gives you a remainder of 8.

or so I think...

[nothing]

The number is between the range 0 to 9

[ChefNinja]

18

[jamessan]

You can't unless you are given more information. Here's a little python to show why:>>> for i in range(18,128,10):
... print i%10
...
8
8
8
8
8
8
8
8
8
8
8Basically, any number that ends in an 8 will return 8 when modded by 10.

[nothing]

No. The number will never be bigger than 9 or smallest than 0.

[jamessan]

No, you are wrong. x % 10 divides x by 10 and returns the remainder. The remainder will always be between 0 and 9 inclusive, but x can be any number. In the case of the example you gave us, x % 10 = 8, x can be any number that has an 8 as the ones digit. If x was limited to the numbers 0 through 9, then the result of x % 10 would be x.

[downpour]

Originally posted by jamessan
No, you are wrong. x % 10 divides x by 10 and returns the remainder. The remainder will always be between 0 and 9 inclusive, but x can be any number. In the case of the example you gave us, x % 10 = 8, x can be any number that has an 8 as the ones digit. If x was limited to the numbers 0 through 9, then the result of x % 10 would be x.

so I was right.

[nothing]

The number that will be % 10 is never be greater than 9 or smaller than 0.

[DNAunion2000]

DNAunion: The answer is 8

***********************

8 % 10 = 8

8 / 10 = 0 with a remainder of 8

And 8 is in the range 0 - 9

[jamessan]

Originally posted by nothing
The number that will be % 10 is never be greater than 9 or smaller than 0. Either you're agreeing with part of my earlier explanation,The remainder will always be between 0 and 9 inclusiveor you are still not understanding this correctly.
Let's take a more generic form of the initial equation you gave us, e.g. 'X % 10 = Y'. No matter what X is, be at 8, 34, or 87352, Y will be the one's digit from each number (8, 4, and 2 respectively). This is because of our counting system being base 10. If we were to use hex instead, then X % 16/10 (decimal/hex) = Y, Y would still be the right-most hex digit of X.

[downpour]

Originally posted by nothing
The number that will be % 10 is never be greater than 9 or smaller than 0.

jared@downpour:~$ python
Python 2.2.3+ (#1, Jul 5 2003, 11:04:18)
[GCC 3.3.1 20030626 (Debian prerelease)] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> 48 % 10
8
>>> 58 % 10
8
>>> 68 % 10
8
>>> 208 % 10
8
>>> 2000008 % 10
8
>>>


SO WE ALL GET THIS CLEAR: ANY NUMBER, DIVISIBLE BY 10, THAT HAS A REMAINDER OF 8, CAN BE X. END OF STORY. ARE WE CLEAR?

(ps. this is not trying to piss anyone off, or prove anyone wrong. I want to clarify it, so we all agree on the language that describes what % does)

[jamessan]

Originally posted by DNAunion2000
DNAunion: The answer is 8You can't say that for sure with the information given to us. If there was the stipulation that X had to be within the digits 0 through 9, then you would be correct. Without that stipulation, the correct answer could be 8, 18, 28, 38, ad infinitum.

[DNAunion2000]

DownPour: SO WE ALL GET THIS CLEAR: ANY NUMBER, DIVISIBLE BY 10, THAT HAS A REMAINDER OF 8, CAN BE X. END OF STORY. ARE WE CLEAR?

DNAunion: No. There is only 1 solution that fits all parameters: 8 is the one and only answer.

[DNAunion2000]

jamessan: [DNAunion] You can't say that [the answer is 8] for sure with the information given to us.

DNAunion: Yes, I can.

Jamessan: If there was the stipulation that X had to be within the digits 0 through 9, then you would be correct. Without that stipulation, the correct answer could be 8, 18, 28, 38, ad infinitum.

DNAunion: And that was stipulated....twice. Nothing stated twice (though after the original problem was posted) that x is between 0 and 9. Here's one of those times.

Nothing: The number that will be % 10 is never be greater than 9 or smaller than 0.

DNAunion: That narrows it down to a single solution: 8.

[DNAunion2000]

DNAunion: Here's a sort of mathematical proof.

x % 10 = 8

That means x / 10 = y (a whole number) with a remainder of 8. Since the divisor is 10, that "remainder" is 8/10. That is:

x % 10 = 8

is the same as

x/10 = y + 8/10

Now we multiply through by the common denominator.

10(x/10) = 10(y + 8/10)
x = 10y + 8

We are told that x is an integer between 0 and 9 inclusive. So:

0 <= x <= 9

Since x = 10y + 8, we can plug that into the inequality in place of x.

0 <= 10y + 8 <= 9

Solving this for y:

0 - 8 <= 10y + 8 - 8 <= 9 - 8
-8 = 10y <= 1
-8/10 <= 10y/10 <= 1/10
-0.8 <= y <= 0.10

We know that y is a whole number, so it must be 0: that's the only whole number within that range. So

y = 0

Now we plug that back into our original equation.

x = 10y + 8
x = 10(0) + 8
x = 0 + 8
x = 8

[jamessan]

Originally posted by DNAunion2000
DNAunion: Here's a sort of mathematical proof. Well, I obviously misunderstood that he was providing a limitation for the values of X. At any rate, a couple of us had already shown the range of numbers that could fit X, so pairing that with the added stipulation provides the correct answer as does your proof.

[DNAunion2000]

jamessan: Well, I obviously misunderstood that he was providing a limitation for the values of X. At any rate, a couple of us had already shown the range of numbers that could fit X, so pairing that with the added stipulation provides the correct answer as does your proof.

DNAunion: Just so we are on the same page, my "mathematical proof" wasn't aimed at "proving" me right and others wrong. It was in response to Nothing's original question.

Nothing: x % 10 = 8

How can I know what x is?

DNAunion: To find out what x is, there is a step-by-step mathematical method: one isn't forced into trial and error.


****************************
PS: An estute mathematician may have spotted a "flaw" in my "mathematical proof". That is why I qualified it as being a SORT OF mathematical proof. It works only for whole numbers (hence my statement that y is a whole number). But whole numbers (i.e., integers restricted to being 0 or positive) are what we programmers deal with when we use % so I didn't see any reason to get TOO technical.

[fortytwo]

DNAunion2000... like the proof... reminds me of that quarter where thats all i did

[skidooer]

#include <stdio.h>

int main()
{
for(int i = 0; ; i++) {
if(i % 10 == 8)
printf("%d\n", i);
}

return 0;
}