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THE BIRTHDAY PARADOX

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THE BIRTHDAY PARADOX

how many people it takes for two of them to share a birthday — and the same count for codes and fingerprints

Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.

Three sizes in one archive — from a sheet on the fridge to a poster on the wall.

StandardUS$1.50

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Formats
A4 · A3 · A2
What you get
Print-ready PDFs, one per size, with every letterform converted to outlines — nothing to install, nothing to shift.
Subject
maths · everyone · reference · study

The count assumes 365 days, each of them equally likely. Real birthdays are not spread evenly, and unevenness only makes matches come sooner, so the printed numbers are a cautious upper bound: in life this many people are needed at most, not at least.

A MATCH WITH SOMEBODY AND A MATCH WITH YOU ARE DIFFERENT QUESTIONS

“Are there two people here with the same birthday?” and “is there anybody here with my birthday?” are different questions. The first asks about 253 pairs in a company of 23; the second asks about only the 22 pairs that contain you.

For the second chance to pass one half, 253 people are needed. And here a coincidence worth noticing, which means nothing at all: 253 is both the number of pairs in a company of 23 and the number of people needed for a match with you in particular. Two different counts, one and the same number.

On the sheet

  • The count assumes 365 days, each of them equally likely. Real birthdays are not spread evenly, and unevenness only makes matches come sooner, so the printed numbers are a cautious upper bound: in life this many people are needed at most, not at least.
  • Colour carries meaning, but meaning never rests on colour alone — the sheet reads in black and white.
  • Nothing about how it was made: the sheet carries only what the reader needs.

Printing

  • Three sizes in the archive: A4 — 210×297 mm, A3 — 297×420 mm, A2 — 420×594 mm.
  • All text is converted to outlines. No fonts to install, and nothing shifts on another machine.
  • White background and sparing fills — it prints on a home printer without draining the cartridge.
  • Margins of at least 10 mm: a home printer cannot print to the edge.
  • No stroke thinner than 0.3 mm, so nothing disappears in print.

Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 8 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.

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Free
the birthday paradox chart — printable PDF — Printable Charts