A and B play a game with two six-sided dice. Each die has some red faces and some blue faces. The two dice are thrown simultaneously. If the top face of each die is the same color, A wins, and if they are different colors, B wins. One die has ﬁve red faces and one blue face. How many red faces does the other die have if both players have the same chance of winning?
If there are $r$ red and $b$ blue faces on the second die, then A will win with probability $$\frac56\cdot\frac r6+\frac 16\cdot\frac b6. $$ This is supposed to be $\frac12$, and of course $r+b=6$. Solve these equations.
Once you solved the problem that way, perform an excessive (contactless) facepalm and contemplate why you didn't see the solution right away without computation.