Hi, I'm Jalil!

A CS & Math undergraduate student at National University of Singapore.

🎓 NUS CS & Math
🥉 2x IMO Bronze
🔬 Undergrad Researcher

The Problem I'm working on

Erdös Problem 106

Draw \( n \) squares inside the unit square with no common interior point. Let \( f(n) \) be the maximum possible sum of the side-lengths of the squares. Is \( f(k^2 + 1) = k \)?

Current thoughts / Sketch:

It's easy to show \(f(k^2 + 1) \geq k\) with a simple example and it's conjecture that \(f(k^2 + 1) = k\) holds. Baek et al. showed that if we further assume that sides of all squares are parallel to the sides of the unit square, then the maximum total side length of \(k^2 + 1\) squares is \(k\). See https://arxiv.org/abs/2411.07274.

Date: Dec 25, 2025

Random Updates

  • May 2026: Started the RIPS 2026 summer research program.
  • May 2026: Completed my UROP project on the Polynomial Freiman–Ruzsa Theorem.