Question 1 : As shown in the picture, four men are in a room, two each wearing black hats and two wearing white hats. Conditions: No one knows what color they are wearing, and they cannot see the hat on their head. They cannot take it off to look at it, they cannot ask each other, and they cannot look back. There is no chance guessing. There is a door in front of Student A and he cannot see the other side.
Q: Anyone who knows the color of their hat, please raise your hand. After a while, a boy raised his hand. Who is he? Why?
Analysis:
1. In terms of algorithms, you cannot ask each other or look back, which means that you cannot sort and compare, and the position cannot be changed.
2. The most intuitive idea is that you can judge your own color by knowing two other people of the same color. However, in this question, the position remains unchanged and the line of sight is in one direction. Only student D can see two, and no one else can see two. Student D only saw different colors, so no one knew which two students had the same color. Classmate D is special
Answer: C.
Reason: Note that the question says that it took a while for someone to raise their hands. This is an implicit message. No one raised their hands, which means that no one can determine their own color. As mentioned just now, the most special thing is Student D, he can see the colors of two people, but after a while, classmate D has not raised his hand, which means that the colors of the two people D saw are different, that is, B and C are different, and C can see To B is white, so C是黑色.
In addition, until now, C only knows that its color is black, but it still does not know the color of D, because it is impossible to know the color of A.
Question 2 : In a deck of playing cards , 10 of them are face up and the rest are face up. Without looking at it, I don’t know which card is face up or back. How do you divide the cards into two piles so that they are face up? There are the same number of upwards.
Analysis: Don’t think in a fixed way. The cards can be turned over. They are either front or back, either 0 or 1. This is the key to answering this question.
Answer: Choose 10 cards to make a pile, and the rest to make a pile. Just turn over the pile of 10 cards.
Reason: Among the 10 cards, there are n front faces and 10-n back faces, so there are 10-n front faces in the other pile. When the 10-card pile is turned over, there will be 10-n front faces.
Question 3 : The boss gives a certain amount of gold as a salary to the employee. If he works for seven days, he will give 1/7 as salary every day. It cannot be in arrears or in advance. The boss can only get 2 dollars, how to divide it? How to pay every day?
This question was a written test question issued by Microsoft back then!
Answer: The first cut cuts one-seventh of the whole piece of gold, the second cut cuts two-sevenths of the whole piece of gold, and the remaining four-sevenths is one portion. Reason
: Give him seven of your cut pieces on the first day. For that one-seventh, give him the two-sevenths you cut up on the second day, and ask him to return the one-seventh you paid him on the first day. On the third day, give him the seventeenths he returned. 1. On the fourth day, give him four-sevenths of the remaining land and get back the two gold bars you gave him before. On the fifth day, give him one-seventh of the gold bars you want back. On the sixth day , if you want one-seventh back, give him two-sevenths of the piece. On the seventh day, give him the last piece and you’ll have
a vivid answer. It’s so funny.
Question 4: Three young men fell in love with a girl at the same time. In order to decide which of them could marry the girl, they decided to have a duel with pistols. Xiao Li's hit rate is 30%, Xiao Huang is better than him, his hit rate is 50%, the best shooter is Xiao Lin, he never makes mistakes, his hit rate is 100%. Because of this obvious fact, for the sake of fairness, they decided to go in this order: Xiao Li shot first, Xiao Huang second, and Xiao Lin last. And then cycle like this until they only have one person left. So who among these three has the best chance of survival? What strategies should they all adopt?
Answer:
Xiao Lin must kill Huang if it is his turn and Xiao Huang is not dead, and then challenge rookie Li in a duel.
Therefore, Huang must hit Lin if Lin is not dead, otherwise he will die.
After Xiao Li calculates and compares (the process is omitted), he will decide to fight Xiao Lin first.
So after calculation, Xiao Li has 873/2600≈33.6% vitality;
Xiao Huang has 109/260≈41.9% vitality;
Xiao Lin has 24.5% vitality.
Oh, in this case, Xiao Li's first shot will be fired into the sky. From now on, he will of course shoot the enemy, whoever is alive will be shot.
Xiao Huang will shoot Lin first as always, and Xiao Lin should kill Huang first. Enemies are on a narrow road!
In the end, the survival rate of Li, Huang, and Lin was about 38:27:35;
the rookie had a higher chance of surviving and winning the beauty.
Li will shoot an empty shot first (if he joins forces to attack Zhong Lin, he will suffer the most). Huang will choose Lin to take a shot. (If he doesn't take Lin, he will definitely finish the game first.) Lin will choose Huang to take a shot (after all, it has a high hit rate). Li Huang duel 0.3: 0.280.4 Possibility of Li Lin duel 0.3:0.60.6 Possibility of success rate 0.73
Li Hehuang vs. Lin Li Huang duel 0.3:0.40.7 0.4 Possibility of Li Lin duel 0.3:0.7 0.6 0.70.7 0.6 Possibility of success rate 0.64