3人帽子题 
及格分有了
组合极值
简单图论
线性汉诺塔 
5人帽子题
Five wise men sit on a bench. They face the same direction, each wearing a hat. Each wise man can only see the hat of the person in front of him, but not his own hat or the hat of the person behind him. They know there are 7 hats in total, 3 black, 1 white, and 3 red. Randomly select 5 hats for the five wise men to wear. First ask the fifth person (he can see the four people in front): Can you determine the color of your hat? "He said yes, then ask the fourth person, the third person, the second person, and the first person in turn. What will they say? (You can only say yes or no) Among the first 4 people, are there some people who can determine the color of their hats no matter what? Please guess the color of their hats
凯文猜数
Kevin plays a computer game. There are N consecutive natural numbers from 1 to N. min=1
The program randomly selects 2 numbers at the beginning. Kevin guesses 1 number each round.
The program tells
1 Guess correctly
2 Greater than all the selected numbers
3 Smaller than all the selected numbers
4 Between two numbers
Kevin hopes that the strategy can ensure that 2 numbers are determined in no more than M rounds in all cases
1 Find the optimal strategy
And M under the strategy?
There are N consecutive natural numbers from 1 to N
When M=2, what is the maximum value of n allowed
结论：显著弱于o3mini high grok 3R,强于R1.
