100 people are on the same field, and each of them wears a hat with a color ( only 2 kinds of colors ). Each of them can see all the distribution of the colors except his/her own. Now each person has to guess the color of his/her own hat, on the same time. State a strategy that could ensure the most people alive after the game.
Strategy 1: Make everyone guess the same color no matter what. ( Obviously will ensure 0 )
Strategy 2: Make everyone guess the color which is of the majority ( or even minority if you wish ) he / she can see. ( Think about it if you see 49 / 50 )
Strategy 3: Let's think about smaller cases, how many people can we ensure when there are only 2 people? You might come up to that make one person guess that "Our hat has different color", and the other guess "Our hat has the same color". Well done, 50%, same it is when scale is enlarged to 100.
Strategy 4: Think about what is the general value in the whole game. Yes, it is the oddity of the distribution. This is another 50% method.