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Birthday Paradox Classroom

Set the room size, reveal birthdays one desk at a time, and watch why 23 students already pushes the odds past 50%.

The Big Idea

One classroom creates far more birthday comparisons than most people expect.

The trick is not asking, "Who matches my birthday?" It is asking, "Do any two students in the room match each other?" As the room grows, the number of possible pairs explodes.

With 23 students there are already 253 different birthday pairs to compare.

Room Size 23 students

Changing the room size reseats everyone with fresh random birthdays.

Students 23
Birthday Pairs 253
Chance Of A Match 50.7%
Chance All Are Unique 49.3%

Reveal The Room

Click desks to flip each birthday

Start clicking desks. A match only counts after both birthdays have been revealed.

Next Click

The next student's chance of matching

0.0%

With no birthdays revealed yet, the next click cannot match anything.

0 / 365 birthdays are currently match targets.

Live Discovery

What is already on the board

Revealed 0 / 23
Matched Dates 0
First Duplicate None yet

Behind The Scenes

The math works by counting unique rooms first.

If every student must land on a different birthday, each new student has fewer safe dates left. Multiply those shrinking fractions together, then subtract from 100%.

No-match formula

Model assumption: 365 equally likely birthdays, ignoring leap day and real-world birthday clusters.

Reveal Log

What your clicks have uncovered

Each click logs what happened in reveal order, so students can watch when the first duplicate appears.