I need a scheme to encode ~50 *unique* identifiers that can be applied to a variety of objects.
None will be smaller than say half a sugarcube.
It isn't safe to assume there will be more than one "surface" available to display the identifier.
All will see a fair bit of "inconsiderate" wear-and-tear. But, keeping a mapping of identifiers to actual identities would let a knowledgeable person reapply a damaged identifier.
The identifier has to be unambiguously recognizable by developmentally disabled individuals -- possibly with collaboration from other such individuals. Consulting a "supervisor" would be a significant disadvantage of any implementation.
I first thought of color codes on resistors. But, those have "placement significance" -- the first band is in a particular location and affects the interpretation of the identifier. That's too high of a cognitive load to avoid confusion and misidentifications.
[They also assign significance to the colors and band position which is of no value, here -- "red black" is JUST "red black" with no other significance, particularly to green black, red green, etc.]
The material on which the colors will be applied may vary in color and composition/texture. Over time/abuse, it is likely that portions of the "identifier" may disappear and need to be reapplied. Or, become soiled.
I plan on using Testor's model paint (enamel) with a clearcoat to help protect it. So, the available colors are what comes out of the bottles (I have no desire to be MIXING colors to get a particular shade/hue/tint/etc)
I first settled on a set of colors that, hopefully, avoid any ambiguity between themselves (is that orange or red?). And, would (hopefully) stand out against an unknown background color. And, in dubious lighting conditions.
[I don't worry about color vision deficiencies as I assume a nearby "peer" will be able to correct any obvious recognition problems]
White, black (?), red, yellow, green, blue.
So, obviously, multiple color spots are required to form an identifier. With 6 colors, one could have hundreds of possible permutations. But, that relies on having an order of interpretation. So, BLACK RED is not misinterpreted as RED BLACK.
I thought of adding a third mark that was only interpreted in a particular position. E.g., RED BLACK GOLD and GOLD BLACK RED are identical -- just "parsed" in different orders.
Restricting the third position to just "GOLD" is wasteful. So, it could be augmented to allow other colors -- SILVER?
So, GOLD X Y and SILVER X Y give two different variations for each color pair (X Y). Picking X&Y from a set of just
*5* colors would give me 50 unique identifiers. With the six colors above, I'd have 72 -- more than needed. I.e., being able to implicitly define an "interpretation order" allows me to deal with permutations instead of combinations!
In an attempt to reduce the number of "spots" ("bands"), I could increase the number of colors but constrain their COMBINATIONS to avoid duplicates introduced by permutations (e.g., BLACK can only be followed by RED, GREEN, BLUE, WHITE or YELLOW; RED can only be followed by GREEN, BLUE, WHITE or YELLOW; etc.). In this way XXXXX BLACK can always be unambiguously mapped to BLACK XXXXX.
If I can reduce the number of spots/bands to *two*, I suspect there would be fewer problems interfacing with these folks; BLACK YELLOW RED might be a legal combination but BLACK RED YELLOW might also be. So, someone mixing up the extra color bands could distort the identifier.
C(n,2) >= 50 implies n needs to be ~10. This starts to look closer to a resistor color code and perhaps adds the potential for "color confusion" ("Is that a red or an orange?" "Grey or light black/dirty white?" "Violet or brown?"). Using SILVER and GOLD to augment the previously mentioned set of six colors could be a viable alternative. But, still leaves me short at 8 colors for 28 combinations.
Is there another way of looking at this that doesn't violate the constraints I've laid out, above?