Each of four people wear a hat with a distinct positive integer $<28$. Everyone can see everyone’s number except his own. At 12:00 pm everyone can say something: either “Red” or “Yellow” or nothing. After 12:00 everyone must know his own number. How can they achieve this?
Source: Brilliant
Let's assume they are around a round table. For each participant X, let $A$ be the guy to his left, $B$ the guy in front, $C$ to his right. Let's write the numbers on the hats in basis $3$: $$n_X=x_2*9+x_1*3+x_0.$$ So $X$ says the number $a_0+b_1+c_2 \pmod 3$ (red=0, yellow=1, nothing=2).
He hears from $A$ the number $b_0+c_1+x_2 \pmod 3$. Since he already knows $b_0,c_1$, that tells him $x_2$.
He hears from $B$ the number $c_0+x_1+a_2 \pmod 3$. Since he already knows $c_0,a_2$, that tells him $x_1$.