Show that if you paint 6 dots on the unit square, then there is always a couple of 2 points with distance <=2/3
88496
Out of 6 points in the interior of a square of sidelength 3, two are at distance less than 2
142692
Point inside a square
39156
Concerning what is between two consecutive squares.
138081
How to determine whether a number can be written as a sum of two squares?
94218
Showing $d(x,y) = \frac{|x-y|}{1+|x-y|}$ is a distance.
99417
An inequality about the sum of distances between points : same color $\le$ different colors?
106791
27 squares of side $1$ inside a circle of radius $2$: Show that three squares share an interior point.
138890
Cool property of the number $24$
118766
For $A_1 A_2\cdots A_{11}$ a regular $11$-gon with circumradius $2$, and point $P$ at distance $3$ from the center, find $\sum PA_k^2$
46760
To show that $P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$
152236
What is the optimal path between $2$ fixed points around an invisible obstructing wall?
156669
Trying to prove a simple (?) inequality
35864
Playing with numbers form $1$ to $n^2$ in an $n\times n$ grid
92106
Prove that $n$ is a sum of two squares?
42744
Prove a number is even using the Pigeonhole Principle
23203
Euclidean distance proof
104527
Prove that there are two subsets of any cardinality-10 subsets of $\{1,2\dots,106\}$ that sum to the same number