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How many rounds does 2013 take to reach the kaprekar constant?
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How many rounds does 2013 take to reach the kaprekar constant?
Understanding Kaprekar's Constant
Kaprekar's constant is 6174, a fascinating number in number theory. It can be reached through a specific process involving any four-digit number that has at least two different digits.
Steps to Reach Kaprekar's Constant from 2013
1. Arrange the digits
- Take the number 2013 and arrange its digits in descending order:
- 3210
2. Arrange in ascending order
- Now, arrange the same digits in ascending order:
- 0123
3. Subtract the two results
- Calculate:
- 3210 - 0123 = 3087
4. Repeat the process
- Now, take 3087:
- Descending: 8730
- Ascending: 0378
- Subtraction: 8730 - 0378 = 8352
5. Continue until reaching 6174
- For 8352:
- Descending: 8532
- Ascending: 2358
- Subtraction: 8532 - 2358 = 6174
6. Final Result
- Once you reach 6174, the process stabilizes, and any further operations will always yield 6174.
Rounds Taken
- The number 2013 takes 3 rounds to reach the Kaprekar constant 6174.
Conclusion
The journey from 2013 to the Kaprekar constant showcases the beauty of numbers and the intriguing patterns they form through simple operations.
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Cheese makers make cheese primarily in factories.(19)They test the milk first.(20) If the cheese has any impurities, the milk is promptly discarded. The milk is then processed and heated at a certain temperature. This is a very lengthy process but a very important process, nonetheless.Then, they have to add salt(21) to the boiled milk in the correct proportion. This turns the milk into cheese. If too much salt is added, then the cheese becomes hard. If too little is added, then the cheese does not set properly.Then they age the cheese for many years(22). This process again cannotbe hurried up.They keep the cheese(23) in round moulds.They sell the cheese in stores(24) after it has been properly aged.You can buy this cheese at any good store(25). Even though it is aged, cheese comes with an expiry date. We should check it before buying.You need to pay a high price for good quality cheese(26), but it is definitely worth it.Q.choose the opposite voice of the ones underlined in the passage no. 22.

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How many rounds does 2013 take to reach the kaprekar constant?
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