Question

Can you help me out with a distribution algorithm?

Here’s the deal. I have Number of pens = (Number of students * Pens per student)
So, if I have 18 students and every student has 3 pens, then we have 54 pens in total.
Every pen has an order number on it like: Pen1, Pen2, Pen3. We have to evenly distribute number of pens to every student by serpentine like this:
(Assuming 18 students)

if 1 pen per user:
person 1: pen 1
person 2: pen 2
person 3: pen 3
…
person 18: pen 18

2 units:

person 1: pen 1 and pen 36
person 2: pen 2 and pen 35
person 3: pen 3 and pen 34
…
person 18: pen 18 and pen 19
3 units:

1st person: unit 1, unit 36, unit 37
2nd person: unit 2, unit 35, unit 38
3rd person: unit 3, unit 34, unit 39
…
person 18: unit 18, unit19, unit54
4 units per student:

person 1: unit 1, unit 36, unit 37, and unit 72
person 2: unit 2, unit 35, unit 38, and unit 71
person 3: unit 3, unit 34, unit 39, and unit 70
…
person 18: unit18, unit19,unit 54, unit 55

So, input is Number of students + pens per student. And I need to output a distribution (array)

Answer 1

This is the Serpentine System.

The following table will tell you which pens to give to each person:

person        Pen 1          Pen 2             Pen 3         Pen 4
  1       PERSONS*0+1    PERSONS*2-0       PERSONS*2+1   PERSONS*4-0
  2       PERSONS*0+2    PERSONS*2-1       PERSONS*2+2   PERSONS*4-1
  3       PERSONS*0+3    PERSONS*2-2       PERSONS*2+3   PERSONS*4-2
  4       PERSONS*0+4    PERSONS*2-3       PERSONS*2+4   PERSONS*4-3
  :
  :
  N       PERSONS*0+N    PERSONS*2-(N-1)   PERSONS*2+N   PERSONS*4-(N-1)
                  ^              ^                 ^             ^
                  |              |                 |             |
                  +--- start at 0 and increase 2 every 2 pens ---+---> 4, 6, 6, 8

And so on in both directions.