My example:

Dima and Trap Graph
Jump (J)
King's rout
Task processing

(From easy to hard)

Just a few more triangles

One beautiful task I've encountered is Friend from IOI 2014.
The idea is so simple and elegant, yet pretty hard to come up with on your own.
It was fully solved only by 13 participants during the contest.

(Random order)
456A - Laptops
429E - Points and Segments
364D - Ghd
226D - The table

My first guess will go to "Planar drawing" from last contest on last Petrozavodsk camp (that contest was used as part of OpenCup, so statement is googleable). Once you understand solution it sounds very logical, but at first sight it seems like a crazy idea to use what is used in that problem.

This answer to similar question on quora by misof is interesting!

Problem link: https://jutge.org/problems/P33851_en

Short statement: Given a string s, count the strings of length n which contain s at least once. The strings (including s itself) must contain only letters chosen among the first m letters from the English alphabet. The result must be printed modulo 10⁹ + 7.

Constraints: 1 ≤ |s| ≤ 10, |s| ≤ n ≤ 10⁹, 1 ≤ m ≤ 26

Solution:

My code: https://github.com/srgrr/JutgeContests/blob/master/P33851_en.cpp

Beautiful Fibonacci Problem from the last div 1 contest Amazed by the solution

Nice one

Counting the number of undirected graphs that all degree of its vertices are even.