…
..
problem-1-multiples-of-3-and-5	…
problem-2-even-fibonacci-numbers	…
problem-3-largest-prime-factor	…
problem-4-largest-palindrome-product	…
problem-5-smallest-multiple	…
problem-6-sum-square-difference	…
problem-7-10001st-prime	…
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-12-highly-divisible-triangular-number	…
problem-13-large-sum	…
problem-14-longest-collatz-sequence	…
problem-15-lattice-paths	…
problem-16-power-digit-sum	…
problem-17-number-letter-counts	…
problem-18-maximum-path-sum-i	…
problem-19-counting-sundays	…
problem-20-factorial-digit-sum	…
problem-21-amicable-numbers	…
problem-22-names-scores	…
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-35-circular-primes	…
problem-36-double-base-palindromes	…
problem-37-truncatable-primes	…
problem-38-pandigital-multiples	…
problem-39-integer-right-triangles	…
problem-40-champernownes-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-goldbachs-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-56-powerful-digit-sum	…
problem-57-square-root-convergents	…
problem-58-spiral-primes	…
problem-59-xor-decryption	…
problem-60-prime-pair-sets	…
problem-61-cyclical-figurate-numbers	…
problem-62-cubic-permutations	…
problem-63-powerful-digit-counts	…
problem-64-odd-period-square-roots	…
problem-65-convergents-of-e	…
problem-66-diophantine-equation	…
problem-67-maximum-path-sum-ii	…
problem-68-magic-5-gon-ring	…
problem-69-totient-maximum	…
problem-70-totient-permutation	…
problem-71-ordered-fractions	…
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-77-prime-summations	…
problem-78-coin-partitions	…
problem-79-passcode-derivation	…
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-85-counting-rectangles	…
problem-86-cuboid-route	…
problem-87-prime-power-triples	…
problem-88-product-sum-numbers	…
problem-89-roman-numerals	…
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-95-amicable-chains	…
problem-96-su-doku	…
problem-97-large-non-mersenne-prime	…
problem-98-anagramic-squares	…
problem-99-largest-exponential	…
problem-100-arranged-probability	…
problem-101-optimum-polynomial	…
problem-102-triangle-containment	…
problem-103-special-subset-sums-optimum	…
problem-104-pandigital-fibonacci-ends	…
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-110-diophantine-reciprocals-ii	…
problem-111-primes-with-runs	…
problem-112-bouncy-numbers	…
problem-113-non-bouncy-numbers	…
problem-114-counting-block-combinations-i	…
problem-115-counting-block-combinations-ii	…
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-121-disc-game-prize-fund	…
problem-122-efficient-exponentiation	…
problem-123-prime-square-remainders	…
problem-124-ordered-radicals	…
problem-125-palindromic-sums	…
problem-126-cuboid-layers	…
problem-127-abc-hits	…
problem-128-hexagonal-tile-differences	…
problem-129-repunit-divisibility	…
problem-130-composites-with-prime-repunit-property	…
problem-131-prime-cube-partnership	…
problem-132-large-repunit-factors	…
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-140-modified-fibonacci-golden-nuggets	…
problem-141-investigating-progressive-numbers-n-which-are-also-square	…
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-147-rectangles-in-cross-hatched-grids	…
problem-148-exploring-pascals-triangle	…
problem-149-searching-for-a-maximum-sum-subsequence	…
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-12-as-a-sum-of-inverse-squares	…
problem-153-investigating-gaussian-integers	…
problem-154-exploring-pascals-pyramid	…
problem-155-counting-capacitor-circuits	…
problem-156-counting-digits	…
problem-157-solving-the-diophantine-equation-1a1b-p10n	…
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-172-investigating-numbers-with-few-repeated-digits	…
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-182-rsa-encryption	…
problem-183-maximum-product-of-parts	…
problem-184-triangles-containing-the-origin	…
problem-185-number-mind	…
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-193-squarefree-numbers	…
problem-194-coloured-configurations	…
problem-195-inscribed-circles-of-triangles-with-one-angle-of-60-degrees	…
problem-196-prime-triplets	…
problem-197-investigating-the-behaviour-of-a-recursively-defined-sequence	…
problem-198-ambiguous-numbers	…
problem-199-iterative-circle-packing	…
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-208-robot-walks	…
problem-209-circular-logic	…
problem-210-obtuse-angled-triangles	…
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-219-skew-cost-coding	…
problem-220-heighway-dragon	…
problem-221-alexandrian-integers	…
problem-222-sphere-packing	…
problem-223-almost-right-angled-triangles-i	…
problem-224-almost-right-angled-triangles-ii	…
problem-225-tribonacci-non-divisors	…
problem-226-a-scoop-of-blancmange	…
problem-227-the-chase	…
problem-228-minkowski-sums	…
problem-229-four-representations-using-squares	…
problem-230-fibonacci-words	…
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-243-resilience	…
problem-244-sliders	…
problem-245-coresilience	…
problem-246-tangents-to-an-ellipse	…
problem-247-squares-under-a-hyperbola	…
problem-248-numbers-for-which-eulers-totient-function-equals-13	…
problem-249-prime-subset-sums	…
problem-250-250250	…
problem-251-cardano-triplets	…
problem-252-convex-holes	…
problem-253-tidying-up	…
problem-254-sums-of-digit-factorials	…
problem-255-rounded-square-roots	…
problem-256-tatami-free-rooms	…
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-266-pseudo-square-root	…
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-270-cutting-squares	…
problem-271-modular-cubes-part-1	…
problem-272-modular-cubes-part-2	…
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--areaperimeter-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-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-300-protein-folding	…
problem-301-nim	…
problem-302-strong-achilles-numbers	…
problem-303-multiples-with-small-digits	…
problem-304-primonacci	…
problem-305-reflexive-position	…
problem-306-paper-strip-game	…
problem-307-chip-defects	…
problem-308-an-amazing-prime-generating-automaton	…
problem-309-integer-ladders	…
problem-310-nim-square	…
problem-311-biclinic-integral-quadrilaterals	…
problem-312-cyclic-paths-on-sierpiski-graphs	…
problem-313-sliding-game	…
problem-314-the-mouse-on-the-moon	…
problem-315-digital-root-clocks	…
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-321-swapping-counters	…
problem-322-binomial-coefficients-divisible-by-10	…
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-eulers-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-338-cutting-rectangular-grid-paper	…
problem-339-peredur-fab-efrawg	…
problem-340-crazy-function	…
problem-341-golombs-self-describing-sequence	…
problem-342-the-totient-of-a-square-is-a-cube	…
problem-343-fractional-sequences	…
problem-344-silver-dollar-game	…
problem-345-matrix-sum	…
problem-346-strong-repunits	…
problem-347-largest-integer-divisible-by-two-primes	…
problem-348-sum-of-a-square-and-a-cube	…
problem-349-langtons-ant	…
problem-350-constraining-the-least-greatest-and-the-greatest-least	…
problem-351-hexagonal-orchards	…
problem-352-blood-tests	…
problem-353-risky-moon	…
problem-354-distances-in-a-bees-honeycomb	…
problem-355-maximal-coprime-subset	…
problem-356-largest-roots-of-cubic-polynomials	…
problem-357-prime-generating-integers	…
problem-358-cyclic-numbers	…
problem-359-hilberts-new-hotel	…
problem-360-scary-sphere	…
problem-361-subsequence-of-thue-morse-sequence	…
problem-362-squarefree-factors	…
problem-363-bzier-curves	…
problem-364-comfortable-distance	…
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-373-circumscribed-circles	…
problem-374-maximum-integer-partition-product	…
problem-375-minimum-of-subsequences	…
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-383-divisibility-comparison-between-factorials	…
problem-384-rudin-shapiro-sequence	…
problem-385-ellipses-inside-triangles	…
problem-386-maximum-length-of-an-antichain	…
problem-387-harshad-numbers	…
problem-388-distinct-lines	…
problem-389-platonic-dice	…
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-400-fibonacci-tree-game	…
problem-401-sum-of-squares-of-divisors	…
problem-402-integer-valued-polynomials	…
problem-403-lattice-points-enclosed-by-parabola-and-line	…
problem-404-crisscross-ellipses	…
problem-405-a-rectangular-tiling	…
problem-406-guessing-game	…
problem-407-idempotents	…
problem-408-admissible-paths-through-a-grid	…
problem-409-nim-extreme	…
problem-410-circle-and-tangent-line	…
problem-411-uphill-paths	…
problem-412-gnomon-numbering	…
problem-413-one-child-numbers	…
problem-414-kaprekar-constant	…
problem-415-titanic-sets	…
problem-416-a-frogs-trip	…
problem-417-reciprocal-cycles-ii	…
problem-418-factorisation-triples	…
problem-419-look-and-say-sequence	…
problem-420-2x2-positive-integer-matrix	…
problem-421-prime-factors-of-n151	…
problem-422-sequence-of-points-on-a-hyperbola	…
problem-423-consecutive-die-throws	…
problem-424-kakuro	…
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-430-range-flips	…
problem-431-square-space-silo	…
problem-432-totient-sum	…
problem-433-steps-in-euclids-algorithm	…
problem-434-rigid-graphs	…
problem-435-polynomials-of-fibonacci-numbers	…
problem-436-unfair-wager	…
problem-437-fibonacci-primitive-roots	…
problem-438-integer-part-of-polynomial-equations-solutions	…
problem-439-sum-of-sum-of-divisors	…
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-445-retractions-a	…
problem-446-retractions-b	…
problem-447-retractions-c	…
problem-448-average-least-common-multiple	…
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-455-powers-with-trailing-digits	…
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-mbius-function-and-intervals	…
problem-465-polar-polygons	…
problem-466-distinct-terms-in-a-multiplication-table	…
problem-467-superinteger	…
problem-468-smooth-divisors-of-binomial-coefficients	…
problem-469-empty-chairs	…
problem-470-super-ramvok	…
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-476-circle-packing-ii	…
problem-477-number-sequence-game	…
problem-478-mixtures	…
problem-479-roots-on-the-rise	…
problem-480-the-last-question	…
index.md	…