Problem 431: Square Space Silo
Problem 447: Retractions C
Problem 448: Average least common multiple
Problem 85: Counting rectangles
Problem 132: Large repunit factors
Problem 172: Investigating numbers with few repeated digits
Problem 17: Number letter counts
Problem 322: Binomial coefficients divisible by 10
Problem 56: Powerful digit sum
Problem 62: Cubic permutations
Problem 63: Powerful digit counts
Problem 77: Prime summations
Problem 356: Largest roots of cubic polynomials
Problem 455: Powers With Trailing Digits
Problem 1: Multiples of 3 and 5
Problem 2: Even Fibonacci Numbers
Problem 7: 10001st prime
Problem 3: Largest prime factor
Problem 4: Largest palindrome product
Problem 5: Smallest multiple
Problem 6: Sum square difference
Problem 8: Largest product in a series
Problem 9: Special Pythagorean triplet
Problem 10: Summation of primes
Problem 11: Largest product in a grid
Problem 272: Modular Cubes, part 2
Problem 12: Highly divisible triangular number
Problem 13: Large sum
Problem 14: Longest Collatz sequence
Problem 15: Lattice paths
Problem 16: Power digit sum
Problem 18: Maximum path sum I
Problem 19: Counting Sundays
Problem 20: Factorial digit sum
Problem 21: Amicable numbers
Problem 78: Coin partitions
Problem 23: Non-abundant sums
Problem 24: Lexicographic permutations
Problem 25: 1000-digit Fibonacci number
Problem 26: Reciprocal cycles
Problem 27: Quadratic primes
Problem 28: Number spiral diagonals
Problem 29: Distinct powers
Problem 30: Digit n powers
Problem 31: Coin sums
Problem 32: Pandigital products
Problem 33: Digit cancelling fractions
Problem 34: Digit factorials
Problem 100: Arranged probability
Problem 35: Circular primes
Problem 36: Double-base palindromes
Problem 37: Truncatable primes
Problem 38: Pandigital multiples
Problem 39: Integer right triangles
Problem 40: Champernowne's constant
Problem 41: Pandigital prime
Problem 42: Coded triangle numbers
Problem 43: Sub-string divisibility
Problem 44: Pentagon numbers
Problem 45: Triangular, pentagonal, and hexagonal
Problem 46: Goldbach's other conjecture
Problem 47: Distinct primes factors
Problem 48: Self powers
Problem 49: Prime permutations
Problem 50: Consecutive prime sum
Problem 51: Prime digit replacements
Problem 52: Permuted multiples
Problem 53: Combinatoric selections
Problem 54: Poker hands
Problem 55: Lychrel numbers
Problem 57: Square root convergents
Problem 58: Spiral primes
Problem 59: XOR decryption
Problem 60: Prime pair sets
Problem 61: Cyclical figurate numbers
Problem 64: Odd period square roots
Problem 65: Convergents of e
Problem 66: Diophantine equation
Problem 67: Maximum path sum II
Problem 210: Obtuse Angled Triangles
Problem 68: Magic 5-gon ring
Problem 69: Totient maximum
Problem 70: Totient permutation
Problem 71: Ordered fractions
Problem 79: Passcode derivation
Problem 72: Counting fractions
Problem 73: Counting fractions in a range
Problem 74: Digit factorial chains
Problem 75: Singular integer right triangles
Problem 76: Counting summations
Problem 80: Square root digital expansion
Problem 81: Path sum: two ways
Problem 82: Path sum: three ways
Problem 83: Path sum: four ways
Problem 84: Monopoly odds
Problem 86: Cuboid route
Problem 88: Product-sum numbers
Problem 89: Roman numerals
Problem 87: Prime power triples
Problem 90: Cube digit pairs
Problem 91: Right triangles with integer coordinates
Problem 92: Square digit chains
Problem 93: Arithmetic expressions
Problem 94: Almost equilateral triangles
Problem 110: Diophantine Reciprocals II
Problem 95: Amicable chains
Problem 96: Su Doku
Problem 97: Large non-Mersenne prime
Problem 98: Anagramic squares
Problem 99: Largest exponential
Problem 101: Optimum polynomial
Problem 102: Triangle containment
Problem 104: Pandigital Fibonacci ends
Problem 103: Special subset sums: optimum
Problem 224: Almost right-angled triangles II
Problem 105: Special subset sums: testing
Problem 106: Special subset sums: meta-testing
Problem 107: Minimal network
Problem 108: Diophantine Reciprocals I
Problem 109: Darts
Problem 225: Tribonacci non-divisors
Problem 111: Primes with runs
Problem 112: Bouncy numbers
Problem 113: Non-bouncy numbers
Problem 115: Counting block combinations II
Problem 114: Counting block combinations I
Problem 116: Red, green or blue tiles
Problem 117: Red, green, and blue tiles
Problem 118: Pandigital prime sets
Problem 119: Digit power sum
Problem 120: Square remainders
Problem 126: Cuboid layers
Problem 121: Disc game prize fund
Problem 122: Efficient exponentiation
Problem 123: Prime square remainders
Problem 124: Ordered radicals
Problem 125: Palindromic sums
Problem 127: abc-hits
Problem 128: Hexagonal tile differences
Problem 130: Composites with prime repunit property
Problem 129: Repunit divisibility
Problem 131: Prime cube partnership
Problem 133: Repunit nonfactors
Problem 134: Prime pair connection
Problem 135: Same differences
Problem 136: Singleton difference
Problem 137: Fibonacci golden nuggets
Problem 138: Special isosceles triangles
Problem 139: Pythagorean tiles
Problem 141: Investigating progressive numbers, n, which are also square
Problem 140: Modified Fibonacci golden nuggets
Problem 142: Perfect Square Collection
Problem 143: Investigating the Torricelli point of a triangle
Problem 144: Investigating multiple reflections of a laser beam
Problem 145: How many reversible numbers are there below one-billion?
Problem 146: Investigating a Prime Pattern
Problem 156: Counting Digits
Problem 147: Rectangles in cross-hatched grids
Problem 149: Searching for a maximum-sum subsequence
Problem 148: Exploring Pascal's triangle
Problem 150: Searching a triangular array for a sub-triangle having minimum-sum
Problem 151: Paper sheets of standard sizes: an expected-value problem
Problem 152: Writing one half as a sum of inverse squares
Problem 153: Investigating Gaussian Integers
Problem 154: Exploring Pascal's pyramid
Problem 155: Counting Capacitor Circuits
Problem 157: Solving the diophantine equation
Problem 158: Exploring strings for which only one character comes lexicographically after its neighbour to the left
Problem 159: Digital root sums of factorisations
Problem 160: Factorial trailing digits
Problem 161: Triominoes
Problem 162: Hexadecimal numbers
Problem 163: Cross-hatched triangles
Problem 164: Numbers for which no three consecutive digits have a sum greater than a given value
Problem 165: Intersections
Problem 166: Criss Cross
Problem 167: Investigating Ulam sequences
Problem 168: Number Rotations
Problem 169: Exploring the number of different ways a number can be expressed as a sum of powers of 2
Problem 170: Find the largest 0 to 9 pandigital that can be formed by concatenating products
Problem 171: Finding numbers for which the sum of the squares of the digits is a square
Problem 173: Using up to one million tiles how many different "hollow" square laminae can be formed?
Problem 174: Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements
Problem 175: Fractions involving the number of different ways a number can be expressed as a sum of powers of 2
Problem 176: Right-angled triangles that share a cathetus
Problem 177: Integer angled Quadrilaterals
Problem 178: Step Numbers
Problem 179: Consecutive positive divisors
Problem 180: Rational zeros of a function of three variables
Problem 181: Investigating in how many ways objects of two different colours can be grouped
Problem 357: Prime generating integers
Problem 182: RSA encryption
Problem 183: Maximum product of parts
Problem 184: Triangles containing the origin
Problem 185: Number Mind
Problem 373: Circumscribed Circles
Problem 186: Connectedness of a network
Problem 187: Semiprimes
Problem 188: The hyperexponentiation of a number
Problem 189: Tri-colouring a triangular grid
Problem 190: Maximising a weighted product
Problem 191: Prize Strings
Problem 192: Best Approximations
Problem 194: Coloured Configurations
Problem 193: Squarefree Numbers
Problem 196: Prime triplets
Problem 195: Inscribed circles of triangles with one angle of 60 degrees
Problem 197: Investigating the behaviour of a recursively defined sequence
Problem 198: Ambiguous Numbers
Problem 199: Iterative Circle Packing
Problem 266: Pseudo Square Root
Problem 200: Find the 200th prime-proof sqube containing the contiguous sub-string "200"
Problem 201: Subsets with a unique sum
Problem 202: Laserbeam
Problem 203: Squarefree Binomial Coefficients
Problem 204: Generalised Hamming Numbers
Problem 205: Dice Game
Problem 206: Concealed Square
Problem 207: Integer partition equations
Problem 209: Circular Logic
Problem 208: Robot Walks
Problem 211: Divisor Square Sum
Problem 212: Combined Volume of Cuboids
Problem 213: Flea Circus
Problem 214: Totient Chains
Problem 215: Crack-free Walls
Problem 216: Investigating the primality of numbers of the form 2n2-1
Problem 217: Balanced Numbers
Problem 218: Perfect right-angled triangles
Problem 230: Fibonacci Words
Problem 219: Skew-cost coding
Problem 220: Heighway Dragon
Problem 221: Alexandrian Integers
Problem 222: Sphere Packing
Problem 223: Almost right-angled triangles I
Problem 227: The Chase
Problem 226: A Scoop of Blancmange
Problem 228: Minkowski Sums
Problem 229: Four Representations using Squares
Problem 231: The prime factorisation of binomial coefficients
Problem 232: The Race
Problem 233: Lattice points on a circle
Problem 234: Semidivisible numbers
Problem 235: An Arithmetic Geometric sequence
Problem 236: Luxury Hampers
Problem 237: Tours on a 4 x n playing board
Problem 238: Infinite string tour
Problem 239: Twenty-two Foolish Primes
Problem 240: Top Dice
Problem 241: Perfection Quotients
Problem 242: Odd Triplets
Problem 244: Sliders
Problem 243: Resilience
Problem 245: Coresilience
Problem 246: Tangents to an ellipse
Problem 247: Squares under a hyperbola
Problem 248: Numbers for which Euler’s totient function equals 13!
Problem 250: 250250
Problem 249: Prime Subset Sums
Problem 251: Cardano Triplets
Problem 252: Convex Holes
Problem 253: Tidying up
Problem 254: Sums of Digit Factorials
Problem 256: Tatami-Free Rooms
Problem 255: Rounded Square Roots
Problem 257: Angular Bisectors
Problem 258: A lagged Fibonacci sequence
Problem 259: Reachable Numbers
Problem 260: Stone Game
Problem 261: Pivotal Square Sums
Problem 262: Mountain Range
Problem 263: An engineers' dream come true
Problem 264: Triangle Centres
Problem 265: Binary Circles
Problem 267: Billionaire
Problem 268: Counting numbers with at least four distinct prime factors less than 100
Problem 269: Polynomials with at least one integer root
Problem 271: Modular Cubes, part 1
Problem 270: Cutting Squares
Problem 273: Sum of Squares
Problem 274: Divisibility Multipliers
Problem 275: Balanced Sculptures
Problem 276: Primitive Triangles
Problem 277: A Modified Collatz sequence
Problem 278: Linear Combinations of Semiprimes
Problem 279: Triangles with integral sides and an integral angle
Problem 280: Ant and seeds
Problem 281: Pizza Toppings
Problem 282: The Ackermann function
Problem 283: Integer sided triangles for which the area * perimeter ratio is integral
Problem 284: Steady Squares
Problem 285: Pythagorean odds
Problem 286: Scoring probabilities
Problem 287: Quadtree encoding (a simple compression algorithm)
Problem 288: An enormous factorial
Problem 289: Eulerian Cycles
Problem 290: Digital Signature
Problem 291: Panaitopol Primes
Problem 292: Pythagorean Polygons
Problem 375: Minimum of subsequences
Problem 293: Pseudo-Fortunate Numbers
Problem 294: Sum of digits - experience #23
Problem 295: Lenticular holes
Problem 296: Angular Bisector and Tangent
Problem 297: Zeckendorf Representation
Problem 298: Selective Amnesia
Problem 299: Three similar triangles
Problem 301: Nim
Problem 300: Protein folding
Problem 302: Strong Achilles Numbers
Problem 303: Multiples with small digits
Problem 304: Primonacci
Problem 305: Reflexive Position
Problem 306: Paper-strip Game
Problem 405: A rectangular tiling
Problem 307: Chip Defects
Problem 308: An amazing Prime-generating Automaton
Problem 309: Integer Ladders
Problem 310: Nim Square
Problem 343: Fractional Sequences
Problem 311: Biclinic Integral Quadrilaterals
Problem 312: Cyclic paths on Sierpiński graphs
Problem 313: Sliding game
Problem 314: The Mouse on the Moon
Problem 315: Digital root clocks
Problem 321: Swapping Counters
Problem 316: Numbers in decimal expansions
Problem 317: Firecracker
Problem 318: 2011 nines
Problem 319: Bounded Sequences
Problem 320: Factorials divisible by a huge integer
Problem 323: Bitwise-OR operations on random integers
Problem 324: Building a tower
Problem 325: Stone Game II
Problem 326: Modulo Summations
Problem 327: Rooms of Doom
Problem 328: Lowest-cost Search
Problem 329: Prime Frog
Problem 330: Euler's Number
Problem 331: Cross flips
Problem 332: Spherical triangles
Problem 333: Special partitions
Problem 334: Spilling the beans
Problem 335: Gathering the beans
Problem 336: Maximix Arrangements
Problem 337: Totient Stairstep Sequences
Problem 348: Sum of a square and a cube
Problem 338: Cutting Rectangular Grid Paper
Problem 339: Peredur fab Efrawg
Problem 341: Golomb's self-describing sequence
Problem 340: Crazy Function
Problem 342: The totient of a square is a cube
Problem 354: Distances in a bee's honeycomb
Problem 344: Silver dollar game
Problem 346: Strong Repunits
Problem 347: Largest integer divisible by two primes
Problem 345: Matrix Sum
Problem 355: Maximal coprime subset
Problem 349: Langton's ant
Problem 350: Constraining the least greatest and the greatest least
Problem 351: Hexagonal orchards
Problem 352: Blood tests
Problem 353: Risky moon
Problem 358: Cyclic numbers
Problem 359: Hilbert's New Hotel
Problem 360: Scary Sphere
Problem 361: Subsequence of Thue-Morse sequence
Problem 362: Squarefree factors
Problem 364: Comfortable distance
Problem 363: Bézier Curves
Problem 365: A huge binomial coefficient
Problem 366: Stone Game III
Problem 367: Bozo sort
Problem 368: A Kempner-like series
Problem 369: Badugi
Problem 370: Geometric triangles
Problem 371: Licence plates
Problem 372: Pencils of rays
Problem 374: Maximum Integer Partition Product
Problem 376: Nontransitive sets of dice
Problem 377: Sum of digits, experience 13
Problem 378: Triangle Triples
Problem 379: Least common multiple count
Problem 380: Amazing Mazes!
Problem 381: (prime-k) factorial
Problem 382: Generating polygons
Problem 384: Rudin-Shapiro sequence
Problem 383: Divisibility comparison between factorials
Problem 385: Ellipses inside triangles
Problem 386: Maximum length of an antichain
Problem 388: Distinct Lines
Problem 387: Harshad Numbers
Problem 389: Platonic Dice
Problem 433: Steps in Euclid's algorithm
Problem 390: Triangles with non rational sides and integral area
Problem 391: Hopping Game
Problem 392: Enmeshed unit circle
Problem 393: Migrating ants
Problem 394: Eating pie
Problem 395: Pythagorean tree
Problem 396: Weak Goodstein sequence
Problem 397: Triangle on parabola
Problem 398: Cutting rope
Problem 399: Squarefree Fibonacci Numbers
Problem 401: Sum of squares of divisors
Problem 400: Fibonacci tree game
Problem 402: Integer-valued polynomials
Problem 404: Crisscross Ellipses
Problem 403: Lattice points enclosed by parabola and line
Problem 406: Guessing Game
Problem 407: Idempotents
Problem 409: Nim Extreme
Problem 410: Circle and tangent line
Problem 411: Uphill paths
Problem 432: Totient sum
Problem 412: Gnomon numbering
Problem 408: Admissible paths through a grid
Problem 413: One-child Numbers
Problem 414: Kaprekar constant
Problem 415: Titanic sets
Problem 417: Reciprocal cycles II
Problem 416: A frog's trip
Problem 418: Factorisation triples
Problem 419: Look and say sequence
Problem 445: Retractions A
Problem 420: 2x2 positive integer matrix
Problem 421: Prime factors of n15+1
Problem 422: Sequence of points on a hyperbola
Problem 424: Kakuro
Problem 423: Consecutive die throws
Problem 430: Range flips
Problem 425: Prime connection
Problem 426: Box-ball system
Problem 427: n-sequences
Problem 428: Necklace of Circles
Problem 429: Sum of squares of unitary divisors
Problem 434: Rigid graphs
Problem 435: Polynomials of Fibonacci numbers
Problem 436: Unfair wager
Problem 438: Integer part of polynomial equation's solutions
Problem 439: Sum of sum of divisors
Problem 446: Retractions B
Problem 437: Fibonacci primitive roots
Problem 440: GCD and Tiling
Problem 441: The inverse summation of coprime couples
Problem 442: Eleven-free integers
Problem 443: GCD sequence
Problem 444: The Roundtable Lottery
Problem 449: Chocolate covered candy
Problem 450: Hypocycloid and Lattice points
Problem 451: Modular inverses
Problem 452: Long Products
Problem 453: Lattice Quadrilaterals
Problem 454: Diophantine reciprocals III
Problem 456: Triangles containing the origin II
Problem 457: A polynomial modulo the square of a prime
Problem 458: Permutations of Project
Problem 459: Flipping game
Problem 460: An ant on the move
Problem 461: Almost Pi
Problem 462: Permutation of 3-smooth numbers
Problem 463: A weird recurrence relation
Problem 464: Möbius function and intervals
Problem 465: Polar polygons
Problem 466: Distinct terms in a multiplication table
Problem 467: Superinteger
Problem 469: Empty chairs
Problem 468: Smooth divisors of binomial coefficients
Problem 470: Super Ramvok
Problem 476: Circle Packing II
Problem 471: Triangle inscribed in ellipse
Problem 472: Comfortable Distance II
Problem 473: Phigital number base
Problem 474: Last digits of divisors
Problem 475: Music festival
Problem 477: Number Sequence Game
Problem 479: Roots on the Rise
Problem 478: Mixtures
Problem 480: The Last Question
Problem 22: Names scores