Problem

An exercise whose solution is desired.

See also Alhazen's Billiard Problem, Alhazen's Problem, André's Problem, Apollonius' Problem, Apollonius Pursuit Problem, Archimedes' Cattle Problem, Archimedes' Problem, Ballot Problem, Basler Problem, Bertrand's Problem, Billiard Table Problem, Birthday Problem, Bishops Problem, Bolza Problem, Book Stacking Problem, Boundary Value Problem, Bovinum Problema, Brachistochrone Problem, Brahmagupta's Problem, Brocard's Problem, Buffon-Laplace Needle Problem, Buffon's Needle Problem, Burnside Problem, Busemann-Petty Problem, Cannonball Problem, Castillon's Problem, Catalan's Diophantine Problem, Catalan's Problem, Cattle Problem of Archimedes, Cauchy Problem, Checker-Jumping Problem, Closed Curve Problem, Coin Problem, Collatz Problem, Condom Problem, Congruum Problem, Constant Problem, Coupon Collector's Problem, Crossed Ladders Problem, Cube Dovetailing Problem, Decision Problem, Dedekind's Problem, Delian Problem, de Mere's Problem, Diagonals Problem, Dido's Problem, Dilemma, Dinitz Problem, Dirichlet Divisor Problem, Disk Covering Problem, Equichordal Problem, Extension Problem, Fagnano's Problem, Fejés Tóth's Problem, Fermat's Problem, Fermat's Sigma Problem, Fisher-Behrens Problem, Five Disks Problem, Four Coins Problem, Four Travelers Problem, Fuss's Problem, Gauss's Circle Problem, Gauss's Class Number Problem, Glove Problem, Guthrie's Problem, Haberdasher's Problem, Hadwiger Problem, Halting Problem, Hansen's Problem, Heesch's Problem, Heilbronn Triangle Problem, Hilbert's Problems, Illumination Problem, Indeterminate Problems, Initial Value Problem, Internal Bisectors Problem, Isoperimetric Problem, Isovolume Problem, Jeep Problem, Josephus Problem, Kakeya Needle Problem, Kakutani's Problem, Katona's Problem, Kepler Problem, Kings Problem, Kirkman's Schoolgirl Problem, Kissing Circles Problem, Knapsack Problem, Knot Problem, Königsberg Bridge Problem, Kuratowski's Closure-Component Problem, Lam's Problem, Langford's Problem, Lebesgue Measurability Problem, Lebesgue Minimal Problem, Lehmer's Problem, Lemoine's Problem, Lifting Problem, Lucas' Married Couples Problem, Malfatti's Right Triangle Problem, Malfatti's Tangent Triangle Problem, Married Couples Problem, Match Problem, Maximum Clique Problem, Ménage Problem, Metric Equivalence Problem, Mice Problem, Mikusinski's Problem, Möbius Problem, Money-Changing Problem, Monkey and Coconut Problem, Monty Hall Problem, Mortality Problem, Moser's Circle Problem, Napoleon's Problem, Navigation Problem, Nearest Neighbor Problem, NP-Complete Problem, NP-Problem, Orchard-Planting Problem, Orchard Visibility Problem, P-Problem, Party Problem, Piano Mover's Problem, Planar Bubble Problem, Plateau's Problem, Points Problem, Postage Stamp Problem, Pothenot Problem, Prouhet's Problem, Queens Problem, Railroad Track Problem, Riemann's Moduli Problem, Satisfiability Problem, Schoolgirl Problem, Schur's Problem, Schwarz's Triangle Problem, Sharing Problem, Shephard's Problem, Sinclair's Soap Film Problem, Small World Problem, Snellius-Pothenot Problem, Steenrod's Realization Problem, Steiner's Problem, Steiner's Segment Problem, Surveying Problems, Sylvester's Four-Point Problem, Sylvester's Line Problem, Sylvester's Triangle Problem, Syracuse Problem, Syzygies Problem, Tarry-Escott Problem, Tautochrone Problem, Thomson Problem, Three Jug Problem, Traveling Salesman Problem, Trawler Problem, Ulam's Problem, Utility Problem, Vibration Problem, Wallis's Problem, Waring's Problem

References

Mathematics Problems

Artino, R. A.; Gaglione, A. M.; and Shell, N. The Contest Problem Book IV: Annual High School Mathematics Examinations 1973-1982. Washington, DC: Math. Assoc. Amer., 1982.

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Barbeau, E. J.; Moser, W. O.; and Lamkin, M. S. Five Hundred Mathematical Challenges. Washington, DC: Math. Assoc. Amer., 1995.

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Chung, F. and Graham, R. Erdös on Graphs: His Legacy of Unsolved Problems. New York: A. K. Peters, 1998.

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Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, 1965.

Dudeney, H. E. Amusements in Mathematics. New York: Dover, 1917.

Dudeney, H. E. The Canterbury Puzzles and Other Curious Problems, 7th ed. London: Thomas Nelson and Sons, 1949.

Dudeney, H. E. 536 Puzzles & Curious Problems. New York: Scribner, 1967.

Eppstein, D. ``Open Problems.'' http://www.ics.uci.edu/~eppstein/junkyard/open.html.

Erdös, P. ``Some Combinatorial Problems in Geometry.'' In Geometry and Differential Geometry (Ed. R. Artzy and I. Vaisman). New York: Springer-Verlag, pp. 46-53, 1980.

Fenchel, W. (Ed.). ``Problems.'' In Proc. Colloquium on Convexity, 1965. Københavns Univ. Mat. Inst., pp. 308-325, 1967.

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Gleason, A. M.; Greenwood, R. E.; and Kelly, L. M. The William Lowell Putnam Mathematical Competition, Problems and Solutions: 1938-1964. Washington, DC: Math. Assoc. Amer., 1980.

Graham, L. A. Ingenious Mathematical Problems and Methods. New York: Dover, 1959.

Graham, L. A. The Surprise Attack in Mathematical Problems. New York: Dover, 1968.

Greitzer, S. L. International Mathematical Olympiads, 1959-1977. Providence, RI: Amer. Math. Soc., 1978.

Gruber, P. M. and Schneider, R. ``Problems in Geometric Convexity.'' In Contributions to Geometry: Proceedings of the Geometry-Symposium Held in Siegen, June 28, 1978 to July 1, 1978 (Ed. J. Tölke and J. M. Wills.) Boston, MA: Birkhäuser, pp. 255-278, 1979.

Guy, R. K. (Ed.). ``Problems.'' In The Geometry of Metric and Linear Spaces. New York: Springer-Verlag, pp. 233-244, 1974.

Halmos, P. R. Problems for Mathematicians Young and Old. Washington, DC: Math. Assoc. Amer., 1991.

Honsberger, R. Mathematical Gems I. Washington, DC: Math. Assoc. Amer., 1973.

Honsberger, R. Mathematical Gems II. Washington, DC: Math. Assoc. Amer., 1976.

Honsberger, R. Mathematical Morsels. Washington, DC: Math. Assoc. Amer., 1979.

Honsberger, R. Mathematical Gems III. Washington, DC: Math. Assoc. Amer., 1985.

Honsberger, R. More Mathematical Morsels. Washington, DC: Math. Assoc. Amer., 1991.

Honsberger, R. From Erdös to Kiev. Washington, DC: Math. Assoc. Amer., 1995.

Honsberger, R. In Pólya's Footsteps: Miscellaneous Problems and Essays. Washington, DC: Math. Assoc. Amer., 1997.

Honsberger, R. (Ed.). Mathematical Plums. Washington, DC: Math. Assoc. Amer., 1979.

Kimberling, C. ``Unsolved Problems and Rewards.'' http://cedar.evansville.edu/~ck6/integer/unsolved.html.

Klamkin, M. S. International Mathematical Olympiads, 1978-1985 and Forty Supplementary Problems. Washington, DC: Math. Assoc. Amer., 1986.

Klamkin, M. S. U.S.A. Mathematical Olympiads, 1972-1986. Washington, DC: Math. Assoc. Amer., 1988.

Kordemsky, B. A. The Moscow Puzzles: 359 Mathematical Recreations. New York: Dover, 1992.

Kurschak, J. and Hajos, G. Hungarian Problem Book, Based on the Eötvös Competitions, Vol. 1: 1894-1905. New York: Random House, 1963.

Kurschak, J. and Hajos, G. Hungarian Problem Book, Based on the Eötvös Competitions, Vol. 2: 1906-1928. New York: Random House, 1963.

Larson, L. C. Problem-Solving Through Problems. New York: Springer-Verlag, 1983.

Mott-Smith, G. Mathematical Puzzles for Beginners and Enthusiasts. New York: Dover, 1954.

Ogilvy, C. S. Tomorrow's Math: Unsolved Problems for the Amateur. New York: Oxford University Press, 1962.

Ogilvy, C. S. ``Some Unsolved Problems of Modern Geometry.'' Ch. 11 in Excursions in Geometry. New York: Dover, pp. 143-153, 1990.

Posamentier, A. S. and Salkind, C. T. Challenging Problems in Algebra. New York: Dover, 1997.

Posamentier, A. S. and Salkind, C. T. Challenging Problems in Geometry. New York: Dover, 1997.

Rabinowitz, S. (Ed.). Index to Mathematical Problems 1980-1984. Westford, MA: MathPro Press, 1992.

Salkind, C. T. The Contest Problem Book I: Problems from the Annual High School Contests 1950-1960. New York: Random House, 1961.

Salkind, C. T. The Contest Problem Book II: Problems from the Annual High School Contests 1961-1965. Washington, DC: Math. Assoc. Amer., 1966.

Salkind, C. T. and Earl, J. M. The Contest Problem Book III: Annual High School Contests 1966-1972. Washington, DC: Math. Assoc. Amer., 1973.

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, 1993.

Shkliarskii, D. O.; Chentzov, N. N.; and Yaglom, I. M. The U.S.S.R. Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics. New York: Dover, 1993.

Sierpinski, W. A Selection of Problems in the Theory of Numbers. New York: Pergamon Press, 1964. Sierpinski, W. Problems in Elementary Number Theory. New York: Elsevier, 1980.

Smarandache, F. Only Problems, Not Solutions!, 4th ed. Phoenix, AZ: Xiquan, 1993.

Steinhaus, H. One Hundred Problems in Elementary Mathematics. New York: Dover, 1979.

Tietze, H. Famous Problems of Mathematics. New York: Graylock Press, 1965.

Trigg, C. W. Mathematical Quickies: 270 Stimulating Problems with Solutions. New York: Dover, 1985.

Ulam, S. M. A Collection of Mathematical Problems. New York: Interscience Publishers, 1960.

van Mill, J. and Reed, G. M. (Eds.). Open Problems in Topology. New York: Elsevier, 1990.