There is a set [math]S[/math] of prisoners (possibly infinite). Each prisoner receives either a red hat or a blue hat. Each prisoner can see every other prisoner's hat, but the prisoners are banned from communicating with each other in any way. Subsequently, each prisoner will be asked the colour of their own ... (more) This is one of my favorite problems from my first term of real analysis. This will probably take a few hours. Focus on finding examples, even if you don't have a rigorous proof.
[math]\det [x^2 + y^2, x, y, 1;[/math]
[math]x_1^2 + y_1^2, x_1, y_1, 1;[/math]... (more)