Sorry if you don't like math :) Most of them are math.

http://www.spoj.com/problems/ADACHES2/ (oeis <3)

http://www.spoj.com/problems/ADAGAME4/ (nice nt + game theory + dp)

http://www.spoj.com/problems/ADASETS/ (nice nt)

http://www.spoj.com/problems/CATER/ (dp on tree)

http://www.spoj.com/problems/CRYPTO1/ (not easy nt but many people solved)

http://www.spoj.com/problems/ETFS/ (segmented euler sieve)

http://www.spoj.com/problems/FIBONOMIAL/ (hard to get and prove formula)

http://www.spoj.com/problems/GCDEX/ (nt with euler sieve)

http://www.spoj.com/problems/INS17M/ (very nice inclusion-exclusion with sieve)

http://www.spoj.com/problems/XXXXXXXX/ (2d segment tree, hard to implement :O)

http://mirror.codeforces.com/contest/853/problem/D (observation + dp :P)

http://mirror.codeforces.com/contest/851/problem/D (nice sieve technique)

http://mirror.codeforces.com/contest/839/problem/E (easy to come up with solution but need to implement max-clique efficiently, dp)

https://www.e-olymp.com/en/problems/6455 (segment tree or naive solution with many hardcore optimizations)

https://www.e-olymp.com/en/problems/7414 (keep 26 lazy segment trees, quite useful technique)

https://www.e-olymp.com/en/problems/6449 (use max(a[i])<=300)

https://www.e-olymp.com/en/problems/5 (optimized full search)

https://www.e-olymp.com/en/problems/18 (nice dp)

https://www.e-olymp.com/en/problems/24 (harder version of 25)

https://www.e-olymp.com/en/problems/25 (harder version of 18)

https://www.e-olymp.com/en/problems/114 (nice but easy nt)

https://www.e-olymp.com/en/problems/170 (logical but hard to come up)

https://www.e-olymp.com/en/problems/7482 (nice segment tree with arithmetic progression update)

UPD1. Added more problems + hints

I think many problems on sgu are very interesting. Too bad the site is down.

http://mirror.codeforces.com/problemset/problem/255/D