The king wants to test who is smarter among the three Wang Zizhong, and then take them all down. The king said seriously, "Today, I will let you play and see who plays best."
"than playing?" The eldest prince and the second prince were puzzled. They looked at each other.
"Than to play? That would be great! " The little prince jumped for joy.
The king took out a deck of playing cards from his pocket, took off the king and Xiao Wang, and took off four kings. He divided the remaining 48 cards into three parts, each 16, and gave them to three princes.
The king said, "Don't look at the cards yet. The big prince draws a card from the second prince, the second prince draws a card from the little prince, and the little prince draws another card from the big prince. " After each of the three princes drew a card, they handed it to the king in turn. The king washed all three cards and gave them back.
The king said, "The cards I gave you the first time were all regular. Now, who can tell what cards you drew from others? " What card was taken? "
The three Wang Zigang turned the cards in their hands. The little prince said, "I drew a red heart 3 from my eldest brother and a Zhang Meihua 7 from my second brother."
The second prince asked, "How do you know?"
The little prince held up the cards in his hand and said, "Look, I have four fives, four sixes and four eights in my hand, but there are only three sevens, one Zhang Meihua seven is missing, but one three hearts is added. My father said that the first transaction is routine, so there must be four sevens. "
The king nodded and said, "The little prince is right!"
The big prince didn't believe it. He said, "This is a fool. I can guess again. "
"Play the game again." The king picked out twelve cards of hearts A to Q, and each of them was dealt four cards, so that the three princes could draw again in the same way just now. After drawing the cards, each of them showed all the cards in their hands.
The cards in the big prince's hand are 6, 7, 9 and Q (12); The cards in the hands of the Second Prince are A (1), 5, 10, J (11); The cards in the little prince's hand are 2, 3, 4 and 8.
The eldest prince said first, "I know! The cards in my hand are regular: 7-6 = 1, 9-7 = 2, 12-9 = 3, and their difference is 1, 2, 3, right? "
The little prince shook his head and said, "don't forget, big brother, you have a card in your hand, which was just drawn from the second brother's hand." Your original card does not have this rule. " The big prince and the second prince really can't figure it out.
The little prince said, "The three cards of 6, 9 and 12 in my hand can all be divisible by 3, so the 3 in my hand must have been drawn from my brother."
The second prince asked, "What are the rules of the cards in my hand?"
"The second brother's card was originally 1, 5, 7, 1 1. These numbers (except 1) can only be divisible by 1 and itself. Mathematically, it is called prime number, but 7 was taken away by big brother. " The little prince replied.
The little prince put the cards in his hand and said, "I must have two, four, eight and 10 cards in my hand. My second brother took 10 cards."
"Good answer!" The king picked out seven cards from the playing cards and spread them on the table. At first glance, the third prince has six hearts, which are 2, 4, 6, 8, 10, Q (12), plus a Xiao Wang (representative 14). After the king washed seven cards, he put them back on the table, and asked each prince to choose two cards and quote the sum of the numbers of the two cards.
The eldest prince said, "The sum of my two cards is 12."
The second prince said, "The sum of my two cards is 10."
The little prince said, "The sum of my two cards is 22."
The king asked, "There is one card left on the table. Who can answer me as soon as possible? What is this card on the table? "
The second prince said, "This can be counted. Because 8+4 = 12, 10+2 = 12, eldest brother's cards may be hearts 8 and 4, or hearts 10 and 2 ... "
"Yes, yes." The eldest prince said anxiously, "Because 8+2 = 10 and 6+4 = 10, the second brother may be 8 and 2 hearts, or 6 hearts and 4 hearts ..."
When the little prince saw that his two brothers were guessing, he blurted out, "The card on the table is Q of hearts (12)." The king flipped through the card and saw it.
The eldest prince asked, "third brother, how do you calculate so fast?"
The little prince smiled and said, "This red heart Q (12) doesn't count." The second prince asked strangely, "How do you know if it's not?"
The little prince explained, "The two cards in my hand are hearts 8 and 14 (Xiao Wang), so I'm sure the card on the table is hearts Q (12)."
The second prince shook his head and said, "I think third brother is fooling people?"
The little prince said: "The sum of the two cards of the second brother is 10, and the Q of hearts (12) can't be in the hands of the second brother;" The sum of the two cards of Big Brother is only 12, so the Q of Hearts (12) will not be in Big Brother's hand, and neither do I.. Q of hearts (12) can only be put on the table! "
The king smiled and nodded and said, "The little prince can know the number of cards on the table without counting. What do you think his intelligence is? "
The big prince realized something. He said: "Third Brother is good at thinking and analyzing problems."
2. Make a wild guess. The powerful country sent two messengers to see the king.
A stout messenger said, "We are the kings of a powerful country. I heard that three princes in your country are very clever, so we gave them a small gift. Please accept it. "
Another tall and thin messenger took out two boxes of gold and silver and opened another pocket. There are 30 big round pearls in it.
Like magic, the fat messenger took a black silk from his pocket. He held up the silk and said, "I covered a prince's eyes with this silk, and then someone put pearls in two boxes and silver boxes, one at a time;" Put it in a golden plate, only two at a time, don't put it away, and don't put too much. Clap your hands every time you play it. After putting it away, the blindfolded prince will tell you how many pearls are in the gold box and the silver box within 20 seconds according to the number of times he hears clapping. "
The thin messenger put in a sentence and said, "If you guess right, give these pearls to him as a gift!" " "
The three princes looked at each other, and the second prince said, "I'll guess first." The fat messenger immediately blindfolded the second prince.
When the second prince heard the clap of hands 19, he said to himself, "The key is to find two numbers, and the sum of these two numbers is equal to19; One number is multiplied by 2, the other number is multiplied by 1, and the total is equal to 30. What are these two numbers? "
"Oh, I remember!" The second prince was about to say, when the thin messenger put his hand down and said, "20 seconds is up."
The second prince grabbed the black silk and said, "Put it in the golden box 1 1 time, * * * 22 pearls; Put it in a silver plate for 8 times, and there are 8 pearls, which add up to exactly 30! "
"Although you got it right, it's been more than 20 seconds. It's a pity that this gift can't be given to you!" The words of the fat messenger are neither too hot nor too cold, which is very ugly.
The little prince smiled and said, "I'll try." The fat messenger quickly blindfolded the little prince.
The thin messenger patted the hand of No.21,and the little prince immediately replied, "There are 12 pearls in the silver box and 18 pearls in the gold box, right?" Everybody count. It's not bad at all.
The fat messenger asked with a big smile, "I believe the little prince will not be cheated." Please tell the little prince the algorithm and we will learn a lot. "
The little prince said, "I heard 2 1 clap." If you put all these 2 1 times in a silver box, there will be only 2 1 pearl, with 9 missing. This means that when I put two pearls in the gold box, there must be 9 times in 2 1 time, so I can make up the 9 short ones. "
The little prince whispered to the fat messenger, "Let me tell you a formula:
The number of pearls in the gold box = (30 clapping) × 2; The number of pearls in the silver box = 30- the number of pearls in the gold box. "
"You also guess." The little prince covered the fat messenger's eyes with black silk, then grabbed the pearl and put it in a gold box and a silver box for a while. "Bang, bang ..." He shot 1 1 piece in succession, and then asked the fat messenger, "Tell me how many pearls there are in each piece?"
The fat messenger stammered, "There are 38 pearls in the golden box, but there are … well, what's wrong with your formula?"
"Ha ha." The little prince smiled and said, "One * * *, there are only 30, you count 38. I only shot 1 1 times, that is, I only put 22 shots each time! " And I haven't finished it yet! Remember, clap your hands at least 15 times, otherwise this formula cannot be used! "Everyone laughed together.
3. Look for gems that make the country strong. When the messenger sees that one plan has failed, he will make another plan.
The thin messenger put five shiny boxes on the table, which are numbered from 1 to 5. Boxes 1, 2, and 4 all say "gems are in this box", box 3 says "gems are not in this box" and box 5 says "gems are not in box 1".
The thin messenger pointed to the box and said, "One of the five boxes contains priceless jewels. Ask the prince to guess which box the jewels are in, but each prince can only guess once. Whoever guesses correctly will give the gem to whom, and which prince will guess first! "
"Let me guess first." The big prince pointed to box 2.
The thin messenger quickly opened box 2, which was empty and had nothing.
The little prince stepped forward and asked, "Is everything written on this box true?"
The thin messenger said, "Only one sentence is true."
The little prince pointed to box 3 and said, "The jewels are in this box."
The thin messenger opened box 3, and the gem was in the box, and all the people present praised it in unison.
The thin messenger asked, "How did the little prince know that the jewel must be in Box 3?"
The little prince explained, "The jewel written on box 5 is not in box 1. The jewel written on box 1 must be true in this box, so what is written on boxes 2, 3 and 4 is a lie, while what is written on box 3 is a lie, so the jewel must be in box 3."
4."3 129"
One day, the king suddenly remembered something. He said to the princes, "Your grandparents died young, and you may not remember their age. Who can tell me how old your grandparents lived! "
The second prince asked, "May I ask you some questions?"
The king replied, "Only one can be asked."
"Ah, it's too difficult to guess the age of grandparents by asking a question. I am afraid that even the gods can't do it! " The big prince said to himself.
The king asked the little prince again, "Can you do it?" The little prince nodded, and the big prince and the two kings were surprised.
The little prince said, "Please multiply my grandfather's age by 5, add 6, multiply 20, add my grandmother's age and subtract 365, and tell me the final number."
The king didn't know what the little prince wanted to do, so he did a mental calculation for a while and said, "2884."
The little prince immediately replied, "Grandpa lived to be 3 1 year old and grandma lived to be 29 years old."
The king stood up happily and said, "exactly, these are the two times!" " "
"Why can dad calculate the age of grandparents by calculating a question?" "You can only ask one question. You have to guess the age of two people, but you can't ask them directly. How do you calculate! " The two brothers kept asking the little prince.
The beauty of the little prince is that he asked his father to work out a four-digit number, so that thousands and hundreds of numbers are related to his grandfather's age; The numbers of ten and one are related to grandma's age.
The little prince's algorithm is: grandpa's age is multiplied by 5 to get 31× 5; Add 6 times 20 to get (31× 5+6) × 20; Add grandma's age of 29 and subtract 365 to get (3 1× 5+6 )× 20-365 = 2884. The little prince secretly added 245 to 2884 and got 3 129, where 3 1 is his grandfather's age and 29 is his grandmother's age.
The eldest prince asked, "Why did you add 245 at last?"
The little prince explained that the above formula can be done by another method of multiplication and distribution law:
(31× 5+6) × 20+29-365 = 31× 5× 20+6× 20+29-365 = 31×100+29+/kl. If you add 245,
It turns out that the little prince, like a magician, added a little "disguise" in his calculation, that is, "plus 6 MINUS 365" In fact, these two steps have nothing to do with calculating the age of his grandparents, but to make this calculation more hidden and mysterious. Otherwise, people will see through it at a glance and it will be boring. If you don't believe me, let's change the direct calculation method.
The little prince said to his father, "Please multiply my grandfather's age by 100 and add my grandmother's age to tell me the final figure."
The king will say, "Go get 3 129, good boy!" " You put your grandmother's age at ten or three; Put my grandfather's age at 1000 or 100, it is better to ask how old my grandparents lived! "You see, it's not a bad thing to ask directly?