In every coloring in two colors of the edges of $K_{10} $ there are at least 20 monochromatic triangles.
130751
Lower bound for monochromatic triangles in $K_n$
44394
Coloring a $10×10$ grid
126583
Coloring points on an n-gon
158856
Prove that a graph with the same number of edges and vertices contains one cycle
145818
Edges on an even number of Hamilton cycles
44795
Sum of areas of triangles which have corners which are lattice points with 74 lattice points inside.
37984
Prove a planar graph with all regions having even degree can be colored with 2 colors
19807
Connected graph with colored edges
16016
Coloring dodecahedron
89531
Show that every graph $G$ has a bipartite subgraph with at least half of the edges of $G$
107964
Simple combinatorics problem.
117862
Number of partitions of an $n$-element set into $k$ classes
37754
Number of vertices of a complete graph with $n$ edges
144571
A conjecture including binomial coefficients
7062
Can the complete graph $K_9$, be 2-coloured with no blue $K_4$ or red triangles?
99829
If a plane is divided by $n$ lines, then it is possible to color the regions formed with only two colors.
90618
Color the edges of $K_6$ red or blue. Prove that there is a cycle of length 4 with monochromatic edges.