Školjka - Web archive of math problems

Registration

What is Školjka?

Školjka is a web archive of math problems, a tool intended for primary and high school students training for math contests. It contains thousands of problems from various math contests in recent two decades.

Why Školjka?

Školjka supports searching by categories and difficulty, allowing students to quickly find the exact problems they are interested in. Likewise, Školjka can be helpful to mentors and teachers for preparing lectures.

Selected competitions

News

Marinada '24

I ove godine organiziramo svima nam omiljeno online natjecanje, Marinadu!

Za one koje ne znaju, Marinada je timsko natjecanje koje se održava online, a svake godine bude pregršt zanimljivih zadataka koji su uglavnom slični natjecanjima, ali uvijek se nađu i neka iznenađenja! Natjecanje je otvoreno za sve, a održat će se u nedelju, 13.10.2024. od 10:00 do 20:00.

Okupite svoj tročlani tim i registrirajte se na linku https://skoljka.org/marinada24/. Tamo možete naći i više informacija i pravila natjecanja. Veselimo se svim prijavama i vidimo se u nedjelju!

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We're organizing our favourite online competition once again this year – Marinada!

For those who don’t know, Marinada is a team-based competition held online, filled with plenty of interesting problems that are similar to traditional contests, but there are always a few surprises too! The competition is open to everyone and will take place on Sunday, October 13, 2024, from 10:00 AM to 8:00 PM.

Gather your three-member team and register at the link: https://skoljka.org/marinada24/. We look forward to seeing all your registrations, and we'll see you on Sunday!

Added by arhiva Oct. 1, 2024, 5:18 p.m.

Recently added tasks

1. KFMO zad 2.

Odredite sve funkcije $f:\mathbb{R}\rightarrow\mathbb{R}$ takve da: $f\left(\frac{x}{f\left(\frac{1}{x}\right)}-x^2\right)=0,\quad\forall x\neq0$

4 months, 2 weeks

1. KFMO zad 5.

Odredite sve funkcije $f:\mathbb{Z}\rightarrow\mathbb{Z}$ takve da: $f(a^2)+f(b^2)+f(c^2)=\left(f(a+b)+f(b+c)+f(a+c)\right)f(a+b+c),\quad\forall a,b,c\in\mathbb{Z}$

4 months, 2 weeks

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