Work out pigeonhole principle instantly with clear inputs, formula shown and shareable results.
The pigeonhole principle says n items in m containers force some container to hold at least ⌈n/m⌉. Turning it around, forcing k items into one container requires m(k − 1) + 1 items.
Pigeonhole principle
with n items in m boxes, some box holds ≥ ⌈n/m⌉
Generalised form
to force k in one box you need m(k − 1) + 1 items
Some container holds at least ⌈100/12⌉ = 9.
With 366 possible birthdays, 367 people force a shared birthday — that is the principle with m = 366, k = 2.