Pigeonhole PrincipleThe cheapest existence argument in maths, plus its generalised form.MathematicsIf n objects are placed into m boxes and n is greaterthan m, then some box holds at least two objects.n items, m boxes ⇒ some box holds ≥ ⌈n/m⌉13 peopleTwo share a birth month13 > 12.5 points in a unit squareTwo within √2/2Quarter the square.n + 1 taken from 1 to 2nTwo are coprimeA consecutive pair.THE COMMON MISTAKE✗ Concluding which box is the full one✓ Concluding only that some box isThe principle is a pure existence statement. It names no box and builds nothing,which is exactly why it costs so little to apply.The generalised form: with n objects in m boxes, some box must hold atleast ⌈n/m⌉ of them.Pigeonhole Principlelearnposters.com
Pigeonhole Principle — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Pigeonhole Principle poster

The rule, 3 worked examples, and the mistake everyone makes.

The generalised form: with n objects in m boxes, some box must hold at least ⌈n/m⌉ of them.

Questions about the Pigeonhole Principle poster

What’s on the Pigeonhole Principle poster?
The rule, 3 worked examples, and the mistake everyone makes. If n objects are placed into m boxes and n is greater than m, then some box holds at…; n items, m boxes ⇒ some box holds ≥ ⌈n/m⌉; 13 people = Two share a birth month; 5 points in a unit square = Two within √2/2; n + 1 taken from 1 to 2n = Two are coprime; Common mistake: Concluding which box is the full one → Concluding only that some box is. The generalised form: with n objects in m boxes, some box must hold at least ⌈n/m⌉ of them.
Who is the Pigeonhole Principle poster for?
Pigeonhole Principle belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning discrete mathematics can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Pigeonhole Principle poster?
When a problem asks you to show that two of something must coincide. A wall chart earns its place by being glanceable from where the work is happening, so Pigeonhole Principle belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Pigeonhole Principle?
The Binomial Theorem, Counting Principles and Euler & Hamiltonian Paths sit alongside Pigeonhole Principle in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.The Binomial TheoremCounting PrinciplesEuler & Hamiltonian Paths
Is the Pigeonhole Principle poster free to download and print?
Yes. Pigeonhole Principle downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Pigeonhole Principle poster print at?
Pigeonhole Principle is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Pigeonhole Principle loses nothing.Printing guide

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