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Thanks for any help one can give with this…

I need a general equation for the following problem, and I am sure it’s a special case of Poisson or binomial or Bernoulli or something, but I can’t seem to rearrange the equations to get the answer I need.

I have:

  • N objects where:

  • A pool of barcodes of size X, where the barcode is assigned randomly for each object from a range of 1 to X barcodes.

  • There is no “memory” of what barcodes were last assigned, and there is no depleting of barcodes, so the pool of barcodes is “replenished” for each assignment of a barcode to an object.
  • Each object gets only one barcode.

The question: What is the range size of barcodes (1 to X) that ensures that there is a given confidence that no two or more objects are tagged with the SAME barcodes ?

My objective is to make the library of barcodes as SMALL as possible to ensure I don’t repeat barcodes on objects with a given confidence.

  • 2
    Questions like this are analyzed in computer science, see [Hash table](http://en.wikipedia.org/wiki/Hash_table) or [Birthday attack](http://en.wikipedia.org/wiki/Birthday_attack), ...2012-08-18

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