I have 100 students, and they all need colored pencils.
Each of them needs the same colors of pencils, however, they can have different shades of the color.
What's the least amount of color and shade combinations I need to purchase so that each student has a unique combination of shades?
So for example, if I decide 10 colors and 10 shades, Student 42 will have (I assigned the shades randomly)
- Color Green Shade A
- Color Red Shade J
- Color Blue Shade C
- Color Orange Shade A
- Color Yellow Shade E
- Color Indigo Shade B
- Color Purple Shade D
- Color Violet Shade A
- Color Light Blue Shade F
- Color Magenta Shade G
And I can be 100 percent sure that if given those color / shade combos, I will be able to tell you it's student 42.
But how can I optimize this so I need less color and shade combos (what's the least I need)? And once I have that smallest amount, how do I go about distributing it so it still has a 100% chance of finding the student?