Tough one...

A set of numbers as follows in 5 colums:

1______2______3______4______5
9______8______7______6______-
-______10_____11_____12_____13
17____16_____15_____14______-
-______18_____19_____20_____21

and so on (ignore the - and _ I've included them to make formatting better).

If I asked what column is 18 in, you would say column 2.
The problem is as follows.

Derive a formula which will provide the column any specific number lies in given that the above pattern continues to infinity. i.e. the number x lies in column y.

Good luck.

Originally posted by Lazaraus
A set of numbers as follows in 5 colums:

1______2______3______4______5
9______8______7______6______-
-______10_____11_____12_____13
17____16_____15_____14______-
-______18_____19_____20_____21

and so on (ignore the - and _ I've included them to make formatting better).

If I asked what column is 18 in, you would say column 2.
The problem is as ...[text shortened]... that the above pattern continues to infinity. i.e. the number x lies in column y.

Good luck.

How about this:

y = min(f(x-1)+1,f(-x)+2)

where f(a) = b : 0<=b<=7 and b=a (mod 8)

Originally posted by Acolyte
How about this:

y = min(f(x-1)+1,f(-x)+2)

where f(a) = b : 0<=b<=7 and b=a (mod 8)

That seems to work - well done.
How long did it take you?

Originally posted by Lazaraus
That seems to work - well done.
How long did it take you?

A few minutes. I noticed it was doing something modulo 8, so I wrote out a table and noticed I could get what I wanted as the minimum of two things.