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Book Proofs

A blog for mathematical riddles, puzzles, and elegant proofs

  • The Fiddler
    • 2025
      • Letter Boxed
      • Can you hop to the lily pad?
    • 2024
      • 2025 puzzle
      • Particles in a box
      • Halloween Puzzle
      • Round, round, get a round
      • Tiling a Tilted Square
      • When is a triangle like a circle?
      • Tiling squares
      • Showcase Showdown
      • How many times can you add up the digits?
      • Chessboard race
      • Pancake race
      • Dungeon Master’s Dice
    • 2023
      • Don’t flip out
      • The Likeliest Monopoly Square
      • Picking a speaker at random
      • The slow car chase
      • Pinball probability
      • The weaving loom problem
      • Betting on football with future knowledge
      • Optimal baseball lineup
      • Braille puzzle
      • Making something out of nothing
      • Möbius prism
  • The Riddler
    • 2023
      • How much can you pull out of a hat?
      • Making the fastest track
      • Ellipse packing
      • N Bottles of Beer
    • 2022
      • Riddler Football Playoffs
      • Randomly cutting a sandwich
      • Fall color peak
      • Loteria
      • Shared birthdays
      • Pill splitting
      • Knocking down the last bowling pin
      • Can you keep your marbles?
      • How high should you climb up the tower?
      • Tower of goats
      • Catch the grasshopper
      • Desert escape
      • Tetrahedral dice game
      • Frustrating elevator
      • Cone crawling
      • Visualize the vertex
      • The luckiest coin
      • A cube of primes
      • Polarization Puzzle
      • Vehicular trouble
      • Inscribed hexagons
      • Optimal Wordle
      • Triangle Trek
    • 2021
      • Squid game
      • Evil twin
      • Perfect pursuit
      • Tetrahedron optimization
      • Infinite cake
      • Definitive diffidence
      • Outthink the Sphinx
      • Baking the biggest pie
    • 2020
      • Turning radius
      • Can you eat all the chocolates?
      • Flawless war
      • Polygons with perimeter and vertex budgets
      • Cutting a ruler into pieces
      • Squaring the pentagon
      • Connect the dots
      • Dungeons & Dragons
      • Flip to freedom
      • When did the snow start?
      • Flipping your way to victory
      • Penny Pinching
      • Delirious ducks
    • 2019
      • Mismatched socks
      • Prismatic puzzle
      • Optimal HORSE
      • Quarter flipping on a spinning table
      • Tank counting
      • Thanos snaps
      • Circular conundrum
      • Gift card puzzle
    • 2018
      • Elf music
      • Settlers in a circle
      • Alice and Bob fall in love
      • Beer pong
      • Hand sort
      • Archipelago
      • Tether your goat!
      • Sniff out the spies
      • Pool hall robots
      • Paths to work
      • Card collection completion
      • Hoop hop showdown
      • The number line game
      • Rug quality control
      • A coin-flipping game
      • L-bisector
      • Smudged secret messages
      • Minimal road networks
      • Counting coconuts
      • Nightmare Solitaire
      • Number shuffle
      • The Dodgeball duel
      • Hanging a picture frame
      • Ostomachion coloring
      • Inscribed triangles and tetrahedra
      • Where will the seven dwarfs sleep tonight?
    • 2017
      • Cracking the safe
      • Finding the doctored coin
      • Sticks in the woods
      • A tetrahedron puzzle
      • Is this bathroom occupied?
      • Squaring the square
      • The lucky derby
      • Colorful balls puzzle
      • Pick a card!
      • A supreme court puzzle
      • The troll and the dwarves
      • The honest prince
      • Convex ranches
      • Space race
      • Rope timing
      • Toddler poker
      • Microorganism multiplication
      • Timing a stoplight just right
      • Impromptu gambling with dice
      • Baby poker
    • 2016
      • Fighting stormtroopers
      • Tangled wires
      • The war game
      • Unmasking the Secret Santas
      • The lonesome king
      • Adversarial map coloring
      • Will you be the deciding vote?
      • Rig the election with math!
      • The deadly board game
      • Non-intersecting chessboard paths
      • Betting on the world series
      • Cutting a circular table
      • Randomized team drafting strategy
      • Splitting a hundred dollar bill
      • How many bananas can the camel carry?
      • Baking the optimal cake
      • Can you outrun the angry ram?
      • Pokémon Go Efficiency
      • Should the grizzly eat the salmon?
      • The Traitorous Generals
      • Stop the alien invasion!
      • Random walk with endpoints
      • Cutting polygons in half
      • How to beat Roger Federer at Wimbledon
      • What if robots cut your pizza?
      • The puzzle of the picky eater
      • The blue-eyed islanders
      • The puzzle of the pirate booty
      • Baseball division champs
      • Monsters’ gems
      • Overflowing martini glass
      • Elevator button puzzle
      • Proud partygoers puzzle
  • Tutorials
    • Double-counting, Part 1
    • Double-counting, Part 2
    • Lucky spins in roulette
  • Competition Problems
    • Inscribed triangles and tetrahedra
    • Counting parallelograms
    • A clever integral
  • Homepage

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Topics

  • binomial
  • calculus
  • classics
  • coding
  • complex analysis
  • conic sections
  • counting
  • differential equations
  • dynamic programming
  • dynamics
  • Fiddler
  • game theory
  • generating functions
  • geometry
  • graph theory
  • induction
  • integer programming
  • integration
  • knot theory
  • limits
  • linearity of expectation
  • linear programming
  • logic
  • Markov chains
  • modeling
  • number theory
  • optimization
  • pigeonhole principle
  • probability
  • random walk
  • recursion
  • Riddler
  • spherical geometry
  • statistics
  • symmetry
  • traveling salesman

Categories

  • Competition Problems
  • The Fiddler
  • The Riddler
  • Tutorials

Recent Posts

  • Letter Boxed
  • Can you hop to the lily pad?
  • 2025 puzzle
  • Particles in a box
  • Halloween Puzzle

Recent Comments

  • Gord Hamilton on Tiling squares
  • Sameer Gauria on Letter Boxed
  • Aaron Goldsmith on Squaring the square
  • Laurent on Can you hop to the lily pad?
  • MarkS on Can you hop to the lily pad?
  • The Fiddler
    • 2025
      • Letter Boxed
      • Can you hop to the lily pad?
    • 2024
      • 2025 puzzle
      • Particles in a box
      • Halloween Puzzle
      • Round, round, get a round
      • Tiling a Tilted Square
      • When is a triangle like a circle?
      • Tiling squares
      • Showcase Showdown
      • How many times can you add up the digits?
      • Chessboard race
      • Pancake race
      • Dungeon Master’s Dice
    • 2023
      • Don’t flip out
      • The Likeliest Monopoly Square
      • Picking a speaker at random
      • The slow car chase
      • Pinball probability
      • The weaving loom problem
      • Betting on football with future knowledge
      • Optimal baseball lineup
      • Braille puzzle
      • Making something out of nothing
      • Möbius prism
  • The Riddler
    • 2023
      • How much can you pull out of a hat?
      • Making the fastest track
      • Ellipse packing
      • N Bottles of Beer
    • 2022
      • Riddler Football Playoffs
      • Randomly cutting a sandwich
      • Fall color peak
      • Loteria
      • Shared birthdays
      • Pill splitting
      • Knocking down the last bowling pin
      • Can you keep your marbles?
      • How high should you climb up the tower?
      • Tower of goats
      • Catch the grasshopper
      • Desert escape
      • Tetrahedral dice game
      • Frustrating elevator
      • Cone crawling
      • Visualize the vertex
      • The luckiest coin
      • A cube of primes
      • Polarization Puzzle
      • Vehicular trouble
      • Inscribed hexagons
      • Optimal Wordle
      • Triangle Trek
    • 2021
      • Squid game
      • Evil twin
      • Perfect pursuit
      • Tetrahedron optimization
      • Infinite cake
      • Definitive diffidence
      • Outthink the Sphinx
      • Baking the biggest pie
    • 2020
      • Turning radius
      • Can you eat all the chocolates?
      • Flawless war
      • Polygons with perimeter and vertex budgets
      • Cutting a ruler into pieces
      • Squaring the pentagon
      • Connect the dots
      • Dungeons & Dragons
      • Flip to freedom
      • When did the snow start?
      • Flipping your way to victory
      • Penny Pinching
      • Delirious ducks
    • 2019
      • Mismatched socks
      • Prismatic puzzle
      • Optimal HORSE
      • Quarter flipping on a spinning table
      • Tank counting
      • Thanos snaps
      • Circular conundrum
      • Gift card puzzle
    • 2018
      • Elf music
      • Settlers in a circle
      • Alice and Bob fall in love
      • Beer pong
      • Hand sort
      • Archipelago
      • Tether your goat!
      • Sniff out the spies
      • Pool hall robots
      • Paths to work
      • Card collection completion
      • Hoop hop showdown
      • The number line game
      • Rug quality control
      • A coin-flipping game
      • L-bisector
      • Smudged secret messages
      • Minimal road networks
      • Counting coconuts
      • Nightmare Solitaire
      • Number shuffle
      • The Dodgeball duel
      • Hanging a picture frame
      • Ostomachion coloring
      • Inscribed triangles and tetrahedra
      • Where will the seven dwarfs sleep tonight?
    • 2017
      • Cracking the safe
      • Finding the doctored coin
      • Sticks in the woods
      • A tetrahedron puzzle
      • Is this bathroom occupied?
      • Squaring the square
      • The lucky derby
      • Colorful balls puzzle
      • Pick a card!
      • A supreme court puzzle
      • The troll and the dwarves
      • The honest prince
      • Convex ranches
      • Space race
      • Rope timing
      • Toddler poker
      • Microorganism multiplication
      • Timing a stoplight just right
      • Impromptu gambling with dice
      • Baby poker
    • 2016
      • Fighting stormtroopers
      • Tangled wires
      • The war game
      • Unmasking the Secret Santas
      • The lonesome king
      • Adversarial map coloring
      • Will you be the deciding vote?
      • Rig the election with math!
      • The deadly board game
      • Non-intersecting chessboard paths
      • Betting on the world series
      • Cutting a circular table
      • Randomized team drafting strategy
      • Splitting a hundred dollar bill
      • How many bananas can the camel carry?
      • Baking the optimal cake
      • Can you outrun the angry ram?
      • Pokémon Go Efficiency
      • Should the grizzly eat the salmon?
      • The Traitorous Generals
      • Stop the alien invasion!
      • Random walk with endpoints
      • Cutting polygons in half
      • How to beat Roger Federer at Wimbledon
      • What if robots cut your pizza?
      • The puzzle of the picky eater
      • The blue-eyed islanders
      • The puzzle of the pirate booty
      • Baseball division champs
      • Monsters’ gems
      • Overflowing martini glass
      • Elevator button puzzle
      • Proud partygoers puzzle
  • Tutorials
    • Double-counting, Part 1
    • Double-counting, Part 2
    • Lucky spins in roulette
  • Competition Problems
    • Inscribed triangles and tetrahedra
    • Counting parallelograms
    • A clever integral
  • Homepage
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