Existsforall Academy

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Videos about mathematical proofs, popular puzzles, and math contest-style problems will be posted. Our goal is to help you to become a better thinker by teac...

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Why Factoring Quadratics by Decomposition Works

New Existsforall Paperbacks and Newsletter!

New Existsforall Academy books! Rigorous Elementary Mathematics

Puzzle #20 Making French Toast

Puzzle #19 Ten Prisoners with Hats

Puzzle #18 Prisoners Standing in a Line

Puzzle #17 Prisoners with Coloured Hats

Puzzle #16 Laughing Prisoners

Puzzle #15 Final Difficult Decanting

Puzzle #14 Decanting with Four Containers

Puzzle #13 River Decanting Again

Puzzle #12 Bachet's Classic Decanting

Puzzle #11 Decanting by the River

Puzzle #10 Ten Groups of Marbles

Puzzle #9 Counterfeit Coin

Puzzle #8 Mountain Trip

Puzzle #7 End Where You Start

Puzzle #6 Connect the Boxes

Puzzle #5 Queen Covering

Puzzle #4 Capture Sixteen Pawns

Puzzle #3 Twenty-five Knights

Puzzle #2 Knight's Tour

Puzzle #1 Mutilated Chessboard

Real Numbers are Uncountable by Cantor Diagonalization

Rationals are Countable by Cantor Snake

Infinitely Many Primes of the Form 4n+3

Ramanujan Nagell aka Triangular Mersenne Numbers

561 is a Carmichael Number

Legendre's Formula for a Prime in a Factorial

Eisenstein's Criterion on Cyclotomic Polynomials