登录
Take a pen and write the number 6174 on a piece of paper. It looks just like any other number, doesn't it? But what if I told you that it was a magic number?
Do you think this is a joke? Well, let's see the magic with a quick experiment.
Start with any four-digit number (四位数)—just make sure that at least two of the digits are different. You may use, for example, 2024.
Now arrange (排列) the digits again to make the smallest possible number: 0224. Then arrange the digits to make the largest number: 4220. Let's subtract (减) the smaller number from the larger number: $4220 - 0224 = 3996$.
Go back to the second step and repeat the process: $9963 - 3699 = 6264$; $6642 - 2466 = 4176$; $7641 - 1467 = 6174$. There you have it: 6174!
You can repeat this experiment with another number. What do you end up with? Is it 6174?
This number is known as Kaprekar's constant (卡普耶卡常数). It was named after the Indian mathematician D. R. Kaprekar. He discovered the magic behind this number in the 1900s after performing the above.
Kaprekar had always enjoyed playing with numbers. He was known for his sharp mind. But when Kaprekar showed the magic of 6174 at an international mathematics meeting, many mathematicians thought it was a useless discovery and made fun of him. But he didn't give up. Yet to this day, no scientist can fully tell why this magic works.
21. Which of the numbers can be chosen to start the experiment, 122, 2025 or 3333?
22. Please try to write down the steps of 1234 to reach Kaprekar's constant.
23. What's the nationality of D. R. Kaprekar?
24. What do you think of the mathematician D. R. Kaprekar? Why? Write 30 words or more.
Do you think this is a joke? Well, let's see the magic with a quick experiment.
Start with any four-digit number (四位数)—just make sure that at least two of the digits are different. You may use, for example, 2024.
Now arrange (排列) the digits again to make the smallest possible number: 0224. Then arrange the digits to make the largest number: 4220. Let's subtract (减) the smaller number from the larger number: $4220 - 0224 = 3996$.
Go back to the second step and repeat the process: $9963 - 3699 = 6264$; $6642 - 2466 = 4176$; $7641 - 1467 = 6174$. There you have it: 6174!
You can repeat this experiment with another number. What do you end up with? Is it 6174?
This number is known as Kaprekar's constant (卡普耶卡常数). It was named after the Indian mathematician D. R. Kaprekar. He discovered the magic behind this number in the 1900s after performing the above.
Kaprekar had always enjoyed playing with numbers. He was known for his sharp mind. But when Kaprekar showed the magic of 6174 at an international mathematics meeting, many mathematicians thought it was a useless discovery and made fun of him. But he didn't give up. Yet to this day, no scientist can fully tell why this magic works.
21. Which of the numbers can be chosen to start the experiment, 122, 2025 or 3333?
22. Please try to write down the steps of 1234 to reach Kaprekar's constant.
23. What's the nationality of D. R. Kaprekar?
24. What do you think of the mathematician D. R. Kaprekar? Why? Write 30 words or more.
答案
21. 2025. 根据第三段第一句可知,实验需要从一个四位数且至少有两位数字不同的数开始。
22. Step 1: $4321 - 1234 = 3087$; Step 2: $8730 - 0378 = 8352$; Step 3: $8532 - 2358 = 6174$. 根据第四、五段可知,先将数字排列成最小数与最大数,然后用最大数减最小数,重复该过程。
23. Indian. 根据“It was named after the Indian mathematician D. R. Kaprekar.”可知,他是印度人。
24. I think he was talented and determined. He had a great talent for Maths. Although many other mathematicians made fun of him and his discovery, he didn't mind. He never gave it up. 开放性试题,言之有理且无语法错误即可。
22. Step 1: $4321 - 1234 = 3087$; Step 2: $8730 - 0378 = 8352$; Step 3: $8532 - 2358 = 6174$. 根据第四、五段可知,先将数字排列成最小数与最大数,然后用最大数减最小数,重复该过程。
23. Indian. 根据“It was named after the Indian mathematician D. R. Kaprekar.”可知,他是印度人。
24. I think he was talented and determined. He had a great talent for Maths. Although many other mathematicians made fun of him and his discovery, he didn't mind. He never gave it up. 开放性试题,言之有理且无语法错误即可。
解析
【分析】
本题为英语阅读理解题，需结合原文内容解答四个问题：第21题需明确实验起始数的要求，判断选项是否符合；第22题需掌握卡普耶卡常数的计算规则，按步骤推导；第23题直接查找国籍信息；第24题结合原文描述评价人物。
【解析】
21题：根据原文第三段，实验起始数需满足“四位数且至少两位数字不同”。122是三位数，不符合；2025是四位数且有不同数字，符合；3333是四位数但所有数字相同，不符合，故选择2025。
22题：按卡普耶卡常数规则，步骤为：①将1234重排为最大数4321、最小数1234，计算得4321-1234=3087；②将3087重排为最大数8730、最小数0378，计算得8730-0378=8352；③将8352重排为最大数8532、最小数2358，计算得8532-2358=6174。
23题：根据原文“It was named after the Indian mathematician D. R. Kaprekar.”，可知其国籍为Indian。
24题：结合原文中Kaprekar热爱数字、有数学天赋、面对嘲笑不放弃的特点，组织符合要求的评价即可。
【答案】
21. 2025.
22. Step 1: $4321 - 1234 = 3087$; Step 2: $8730 - 0378 = 8352$; Step 3: $8532 - 2358 = 6174$.
23. Indian.
24. I think he was talented and determined. He had a great talent for Maths. Although many other mathematicians made fun of him and his discovery, he didn't mind. He never gave it up.
【知识点】
英语阅读理解；细节查找；数字规律应用
【点评】
本题围绕卡普耶卡常数及其发现者展开，考查学生信息提取、规则应用和开放性表达能力，需仔细阅读原文获取关键信息。
【难度系数】
0.6
本题为英语阅读理解题，需结合原文内容解答四个问题：第21题需明确实验起始数的要求，判断选项是否符合；第22题需掌握卡普耶卡常数的计算规则，按步骤推导；第23题直接查找国籍信息；第24题结合原文描述评价人物。
【解析】
21题：根据原文第三段，实验起始数需满足“四位数且至少两位数字不同”。122是三位数，不符合；2025是四位数且有不同数字，符合；3333是四位数但所有数字相同，不符合，故选择2025。
22题：按卡普耶卡常数规则，步骤为：①将1234重排为最大数4321、最小数1234，计算得4321-1234=3087；②将3087重排为最大数8730、最小数0378，计算得8730-0378=8352；③将8352重排为最大数8532、最小数2358，计算得8532-2358=6174。
23题：根据原文“It was named after the Indian mathematician D. R. Kaprekar.”，可知其国籍为Indian。
24题：结合原文中Kaprekar热爱数字、有数学天赋、面对嘲笑不放弃的特点，组织符合要求的评价即可。
【答案】
21. 2025.
22. Step 1: $4321 - 1234 = 3087$; Step 2: $8730 - 0378 = 8352$; Step 3: $8532 - 2358 = 6174$.
23. Indian.
24. I think he was talented and determined. He had a great talent for Maths. Although many other mathematicians made fun of him and his discovery, he didn't mind. He never gave it up.
【知识点】
英语阅读理解；细节查找；数字规律应用
【点评】
本题围绕卡普耶卡常数及其发现者展开，考查学生信息提取、规则应用和开放性表达能力，需仔细阅读原文获取关键信息。
【难度系数】
0.6
