Birthday paradox on Slack username colors.

README.md

You might know the birthday problem: “it only takes 23 people so that two have the same birthday”.

But do you know the Slack username color problem?

Slack gives random colors to each user in compact view. But there’s only 51 colors to choose from, so as soon as you are 9 in a channel, odds are that two share the same color.

birthday.jl

function pcol(k, n)
  1 - factorial(big(k)) * binomial(big(n), k) / big(n)^k
end

function mink(n)
  k = 0
  while pcol(k, n) < 0.5
    k += 1
  end
  k
end

println(mink(51))

colors.json

[
  "235e5b",
  "2b6836",
  "385a86",
  "3c8c69",
  "3c989f",
  "43761b",
  "4bbe2e",
  "4ec0d6",
  "50a0cf",
  "53b759",
  "5870dd",
  "5a4592",
  "5b89d5",
  "619a4f",
  "674b1b",
  "684b6c",
  "73769d",
  "827327",
  "8469bc",
  "84b22f",
  "8d4b84",
  "8f4a2b",
  "902d59",
  "965d1b",
  "99a949",
  "9b3b45",
  "9d8eee",
  "9e3997",
  "9f69e7",
  "a2a5dc",
  "a63024",
  "a72f79",
  "aba727",
  "b14cbc",
  "bb86b7",
  "bc3663",
  "bd9336",
  "d1707d",
  "d55aef",
  "d58247",
  "db3150",
  "dc7dbb",
  "dd8527",
  "de5f24",
  "df3dc0",
  "e06b56",
  "e0a729",
  "e475df",
  "e7392d",
  "e96699",
  "ea2977"
]