Get pair number of given shelf number I work at a warehouse, and have shelves organized in that way: (number means shelf number and "--" means aisle between shelves) 1 2 -- -- 3 4 5 6 -- -- 7 8 9 10 -- -- 11 12 etc. Pair 1-3 represent aisle #1, pair 2-4 represent aisle #2, pair 5-7 represent aisle #3 and so on. There is no aisle between 3 and 5 because it's the same shelf. I wonder if there is an elegant formula to get aisle number for a given shelf? Say it must return 1 for 1 or 3, return 2 for 2 or 4, 5 for 9-11 etc.

Ok writing some scripts, drawing big images, and running to my local library counting shelves there hopefully solved this question. Given the Shelf number $s$ you get the aisle by:

$$ a = 2\left\lfloor \frac{s-1}{4} \right\rfloor + ({(s-1)}\mod 2) +1 $$