196-algorithm termination problem | angle trisection problem | bin packing problem | Cauchy problem | chromatic number problem | circle squaring problem | clique problem | Collatz problem | composite number problem | crossing number problem | cube duplication problem | directed Hamiltonian cycle problem | domatic number problem | dominating set problem | feedback arc set problem | feedback vertex set problem | graph genus problem | graph isomorphism problem | halting problem | Hamiltonian cycle problem | ... (total: 85)

The 196-algorithm consists of taking any positive integer of two digits or more, reversing the digits, and adding to the original number. The 196-algorithm termination problem then asks if iterating this procedure starting with the number 196 eventually produces a palindromic number.

The angle trisection problem asks for the division of an arbitrary angle into three equal angles using only a straightedge and compass.

The bin packing problem asks if there exists a partition of a finite set of items U into disjoint sets U_1, U_2, ..., U_k such that the sum of the sizes of the items in each U_i is B or less.

A Cauchy problem asks for the solution of a partial differential equation that satisfies certain conditions which are given on a hypersurface in the domain.

Given a graph on n vertices and a positive integer k<=n, the chromatic number problem asks if the vertices of the graph are colorable by k distinct colors in such a way that no adjacent vertices share the same color.

The circle squaring problem asks for the geometric construction of a square with area equal to that of a given circle using only a straightedge and compass.

Given a graph and a positive integer k, the clique problem asks if the graph contain a clique of size greater or equal to k.

The Collatz problem is determination of if iterating the recurrence a_n = piecewise | a_(n - 1)/2 | a_(n - 1) congruent 0 (mod 2) 3a_(n - 1) + 1 | a_(n - 1) congruent 1 (mod 2) always returns to 1 for positive a_0.

The composite number problem is the determination of if for a given positive integer N, there exist positive integers m and n such that N = mn.

The crossing number problem asks if a given graph has a crossing number of less than or equal to a nonnegative integer k.

| solution angle trisection problem | No such construction is possible. circle squaring problem | No such construction is possible. cube duplication problem | No such construction is possible. halting problem | undecidable handshake problem | (n 2) heptadecagon construction problem | Yes. Hilbert's nineteenth problem | Yes. Kirkman's schoolgirl problem | Sun | ABC | DEF | GHI | JKL | MNO Mon | ADH | BEK | CIO | FLN | GJM Tue | AEM | BHN | CGK | DIL | FJO Wed | AFI | BLO | CHJ | DKM | EGN Thu | AGL | BDJ | CFM | EHO | IKN Fri | AJN | BIM | CEL | DOG | FHK Sat | AKO | BFG | CDN | EIJ | HLM Königsberg bridge problem | No. Monty Hall problem | Yes. (Assuming you prefer to win a car rather than a goat.) queens problem | piecewise | n - 1 | n = 2 ∨ n = 3 n | (otherwise) Smale's fourteenth problem | Yes. social golfer problem | Mon | ABCD | EFGH | IJKL | MNOP | QRST Tue | AEIM | BJOQ | CHNT | DGLS | FKPR Wed | AGKO | BIPT | CFMS | DHJR | ELNQ Thu | AHLP | BKNS | CEOR | DFIQ | GJMT Fri | AFJN | BLMR | CGPQ | DEKT | HIOS

Determine the shape of the boundary and type of equation which yield unique and reasonable solutions for the Cauchy boundary conditions.

Does there exist a function f:V->{1, 2, ..., k} such that f(u)!=f(v) whenever {u, v} element E?

Does G contain a subset V'⊆V with left bracketing bar V' right bracketing bar >=k such that every two vertices in V' are joined by an edge in E?

Is a given positive integer prime?

Can a graph be embedded in the plane with k or fewer pairs of edges crossing one another?

Can the vertex set V of a graph G be partitioned into k'>=k disjoint sets V_1, V_2, ..., V_k' such that each V_i is a dominating set for G?

Is there a subset V'⊆V with left bracketing bar V' right bracketing bar <=k such that for all u element V - V', there is a v element V' for which {u, v} element E?

Given two graphs G_1 = (V_1, E_1) and G_2 = (V_2, E_2), is there a one-to-one function f:V_1->V_2 such that {u, v} element E_1 iff {f(u), f(v)} element E_2?

Sometimes interpreted as: "prove that Peano arithmetic is consistent."

Sometimes interpreted as: "find geometries whose axioms are closest to those of Euclidean geometry if the ordering and incidence axioms are retained, the congruence axioms weakened, and the equivalent of the parallel postulate omitted."

| formal statement Landau's fourth problem | sum_(n=1)^∞Boole(n^2 + 1 element P) = ∞