Euphoric fun at MathsJam Antwerp @MathsJamAntwerp last night, where Simon solved two 2×2 Rubik’s Cube puzzles and one tricky maths problem, and simply enjoyed socialising with like-minded folks. In the video below he explains how he solved the Rubik’s Cube puzzles:
1. Solve the cube so that on every face the 4 colors are all different;
2. Solve the cube so that not only the 4 colors on every face are different but also every face has a different color combination.
After we stopped filming, Simon added that a cube like this has 8! times 3^8 possibilities in total, because the cube has 8 corners and every corner has three orientations.
Simon also talks about the Choose function and symmetries:
Simon showing his solution to university maths students.
Simon also solved a tough problem (one of several tough problems) that asked to sum up the digits in x, if x equals 1111…1111 (number with 100 ones) minus 222…222 (number with 50 twos):
Simon spent the rest of the time trying to prove the ‘cosine rule’, an equation similar to Pythagoras’s theorem, that defines the side c of any triangle if it’s opposite to angle C: c² = a² + b² – 2abcosC. He got stuck with the proof, but luckily, with so many university professors walking around, he got great help from one of them, who came up with an alternative proof using vectors!