Maths Problem

Killerkebab · 15 Feb 2006 at 23:25

Because there are 511,111 digits, which means 85185 numbers remaining, since your sequence is nothing more than a number line.

So what you need is the 85185th number, which you quite rightly said is 185184 (I got it wrong, I guess).

This number will have six digits.
The fraction, 0.16r is one sixth.

So the digit you are looking for will be the 85185th number (185184), and then you go along one sixth of this number, to find your digit, which is still 8.

p4radox · 15 Feb 2006 at 23:34

Killerkebab said:
Because there are 511,111 digits, which means 85185 numbers remaining, since your sequence is nothing more than a number line.

So what you need is the 85185th number, which you quite rightly said is 185184 (I got it wrong, I guess).

This number will have six digits.
The fraction, 0.16r is one sixth.

So the digit you are looking for will be the 85185th number (185184), and then you go along one sixth of this number, to find your digit, which is still 8.

In a way I see what you're saying, but I can't quite get it into my head. Why do you need to go along one sixth of the number to find the 1 millionth digit?

I can see that having 511,111 digits remaining, and dividing this by 6 gives 85185.16r, but why does this mean you have to take the 2nd digit of 185184? Isn't the 1 one sixth of the way along the number?

Killerkebab · 15 Feb 2006 at 23:44

No, the 1 is the very start of the number.
The 8 is one sixth along the number. Let's draw it out:

Basically, a whole number (in our example, 85185) would denote the very beginning of our number.

So when you reach the end of the cycle, i.e: six sixths along the number, you reach the next number.

One sixth along the number thus becomes eight.

I really hope I am not getting this wrong.

Think of it this way, if your answer wasn't 85185.16r, but 85185 on the dot, what digit would you have chosen?

p4radox · 15 Feb 2006 at 23:47

Nah, makes sense. Cheers fella.

carvegio · 16 Feb 2006 at 08:53

The answer is 1, I am pretty sure of that..

I just doubled check it with a quick matlab program.

could have miscounted by one in the prog, I can't check it till work finishes, it might be 8 :O

Rich_L · 16 Feb 2006 at 09:59

I really hope I am not getting this wrong.

You are

Think of it this way, if your answer wasn't 85185.16r, but 85185 on the dot, what digit would you have chosen?

If it was 85185 on the dot, then it would be 99,999 + 6(85185) = 488,889 + 511,110 = 999,999.

So the 85,185th number past 99,999 (185,184) contains the 999,999th digit at the end. So the millionth is the start of the next number, the 1 of 185185