Math Paradoxes, Interactively

What it is

Math Paradoxes, Interactively is a browser-based collection of probability puzzles such as the Monty Hall problem, the German tank problem, the bus paradox, and the 100 prisoners problem. Each puzzle gives you a setup, an interactive experiment, a simulation tool, and several explanations so you can explore why the correct answer feels wrong.

Editor takes

JunoThe Puzzle Purist

“Clear rules, fair mechanics, and earned aha moments — the simulations and multi-angle explanations force you to confront the intuition instead of just accepting the answer.”

NicoThe Commuter

“Each puzzle is a self-contained quick session, but the deep explanations and simulations are more of an afternoon sit-down than a two-minute break on your phone.”

How to play

Choose a puzzle on the homepage and read the setup, noting what your intuition thinks will happen. Play the interactive version and run thousands of simulations in the browser to see the actual distribution. Then go through the explanations, and use the hidden-answer option if you want to test yourself first.

Tips

• Write down your first guess before playing or simulating; you can compare it with the proven result afterward.
• Use the simulation feature to run thousands of trials, especially where the intuitive answer is close to the real one.
• If the first explanation doesn't convince you, try a different one; each puzzle offers multiple ways to look at it.
• Start with the school-level puzzles before the advanced ones, since difficulty is marked.
• Use 'Hide all answers' to challenge yourself before revealing the solution.

Questions