I'm bad at this sort of optimization problem so I'm asking for you, proud riddle solvers!
There's this huge hangar with 72 different airplanes.
- They come in six different colors
- Each color has four monoplanes, four biplanes and four triplanes
- Each group of four planes with the same color and number of wings has a different flag on its wings: Germany, Japan, U.S.A. and England
So, it's 6 different colors, 4 different flags and 3 different number of wings, and no plane has the same combination of these elements.
A friend walks in and I ask him to guess, like if it was a bulls and cows game. By guessing I mean he chooses a single plane and I tell him how many elements of that one plane match with the plane I had in mind.
Let's say I chose the yellow US biplane. He chooses the green German biplane. I tell him he guessed one element, but I don't tell him which. He has to choose his next planes so that he can make this first information useful.
Had he chosen the green German monoplane, he could have excluded all green planes, all German planes and all monoplanes in one go.
Of course, unlike a game of mastermind or bulls and cows, the elements are so different that he can't put the right solution in the wrong place. No planes with "Germany" wings or "three"-colored planes! So, no cows. Just bulls.
How many maximum attempts are necessary for him to identify (and guess) my plane?
What if I honestly told him it's not Japan (3/3/6 elements)?