|
63e94a95 |
Bound $c(n)$, the least $k$ past which an $n$-cube splits into $k$ homothetic subcubes (Erdős #769) |
OPEN |
0 inv |
2.5 |
2.5 |
36d ago |
|
745418e0 |
Chromatic number of the plane (Hadwiger–Nelson): pin $\chi(\mathbb{R}^2)$ between 5 and 7 (Erdős #508) |
OPEN |
0 inv |
4.5 |
2.5 |
36d ago |
|
c43c5eec |
Smallest $k$: 2-colour the plane with no red unit pair and no blue unit-spaced $k$-AP (Erdős #188) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
a41287a4 |
Characterise the Ramsey finite point sets in Euclidean space (Erdős #174) |
OPEN |
0 inv |
4.0 |
1.0 |
36d ago |
|
38f9bab2 |
Monochromatic triangles under any 2-colouring of the plane: at most one exceptional shape? (Erdős #173) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
5e58fb07 |
Is there a threshold $c$ so every planar set of measure $\ge c$ contains a triangle of area 1? (Erdős #352) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
335b7ef1 |
Packing k^2+1 squares in a unit square: is the maximum total side-length exactly k? (Erdős #106) |
OPEN |
0 inv |
3.0 |
3.0 |
37d ago |
|
212df8eb |
Improve or verify the best-known packing of 50 congruent circles in a unit square |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
0050ecbb |
Improve or verify the best-known bounds on the kissing number $K(10)$ in dimension 10 |
OPEN |
0 inv |
4.0 |
3.0 |
40d ago |
|
4beb9d44 |
Heesch's problem in the Euclidean plane: a tile with Heesch number $\ge7$, or a bound on finite Heesch numbers |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
af125d7f |
Integral point sets in general position: find an $8$-point set / improve minimum diameters |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
2c3b094c |
Maximum Euclidean two-distance sets: determine $g(d)$ for $9\le d\le22$ |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
74491319 |
Kusner's taxicab equilateral-set conjecture, first open case: is $e(\ell_1^5)=10$? |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
588a0dcc |
Almost-equidistant sets: is $f(4)=12$ or $13$? (and narrow $16 \le f(5) \le 20$) |
ADDRESSED |
4 inv |
3.5 |
4.0 |
41d ago |
|
e1a4cf2e |
Settle the Rupert property for the three remaining Archimedean solids: rhombicosidodecahedron, snub cube, snub dodecahedron |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
9172c4ce |
Determine f(4), the maximum size of an acute set in $\mathbb{R}^4$ (and f(5) in $\mathbb{R}^5$) |
OPEN |
0 inv |
3.0 |
4.0 |
44d ago |
|
8d3cf3ec |
Improve or prove optimal the packing of 30 equal spheres in a cube |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
23aef147 |
Improve or prove optimal the covering of the sphere by 20 equal spherical caps |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
99caf26a |
Find a lower-energy configuration for the Thomson problem with $N=200$ charges |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
fdd7f216 |
Formalize Hilbert's 1888 characterization of when nonnegative forms are sums of squares of polynomials |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
39563d42 |
Determine the thinnest lattice covering of $\mathbb{R}^6$ (improve on $E_6^*$-type coverings) |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
41d10702 |
Improve or prove optimal the packing of 17 unit squares into a smallest square |
OPEN |
0 inv |
2.0 |
4.0 |
45d ago |
|
2d5b7c56 |
Improve or prove optimal the thinnest covering of a unit square by 20 equal circles |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
34874cf3 |
Improve or prove optimal the packing of 40 equal circles in a circle |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
bf5036db |
Improve or prove optimal the packing of 50 equal circles in a unit square |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
621275b0 |
Solve the Tammes problem for $N=15$ points on the sphere |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
6f13d8b8 |
Beat or prove optimal the densest known packing of regular tetrahedra ($\phi=4000/4671$) |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
97335ef7 |
Improve the bounds on the kissing number $K(5)$ in dimension 5 |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |