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| 1 | +Have you ever played with numbers and found a surprising pattern? One such fascinating pattern is hidden within **Kaprekar's Routine**, named after the Indian mathematician D.R. Kaprekar. It's a simple game that, for most four-digit numbers, always leads to the same result: **6174**. |
| 2 | + |
| 3 | +Let's dive in and see how it works! |
| 4 | + |
| 5 | +## The Rules of the Game |
| 6 | + |
| 7 | +1. **Pick a four-digit number** with at least two different digits. (Numbers like 1111, 2222, etc., won't work). |
| 8 | +2. **Arrange the digits** to form the largest possible number. |
| 9 | +3. **Arrange the same digits** to form the smallest possible number. |
| 10 | +4. **Subtract** the smallest number from the largest number. |
| 11 | +5. **Repeat** steps 2-4 with the new number you get. |
| 12 | + |
| 13 | +You'll be amazed at what happens! |
| 14 | + |
| 15 | +## Example 1: Starting with 3524 |
| 16 | + |
| 17 | +Let's try with the number **3524**: |
| 18 | + |
| 19 | +* **Step 1:** Our number is 3524. It has different digits. |
| 20 | +* **Step 2:** Largest number: 5432 |
| 21 | +* **Step 3:** Smallest number: 2345 |
| 22 | +* **Step 4:** Subtract: 5432 - 2345 = **3087** |
| 23 | + |
| 24 | +Now, we repeat the process with **3087**: |
| 25 | + |
| 26 | +* **Step 2:** Largest number: 8730 |
| 27 | +* **Step 3:** Smallest number: 0378 (remember to include leading zeros to keep it a four-digit number) |
| 28 | +* **Step 4:** Subtract: 8730 - 0378 = **8352** |
| 29 | + |
| 30 | +Repeat with **8352**: |
| 31 | + |
| 32 | +* **Step 2:** Largest number: 8532 |
| 33 | +* **Step 3:** Smallest number: 2358 |
| 34 | +* **Step 4:** Subtract: 8532 - 2358 = **6174** |
| 35 | + |
| 36 | +And there it is! We reached 6174. |
| 37 | + |
| 38 | +## Example 2: Starting with 1987 |
| 39 | + |
| 40 | +Let's try another one with **1987**: |
| 41 | + |
| 42 | +* **Step 1:** Our number is 1987. |
| 43 | +* **Step 2:** Largest number: 9871 |
| 44 | +* **Step 3:** Smallest number: 1789 |
| 45 | +* **Step 4:** Subtract: 9871 - 1789 = **8082** |
| 46 | + |
| 47 | +Repeat with **8082**: |
| 48 | + |
| 49 | +* **Step 2:** Largest number: 8820 |
| 50 | +* **Step 3:** Smallest number: 0288 |
| 51 | +* **Step 4:** Subtract: 8820 - 0288 = **8532** |
| 52 | + |
| 53 | +Repeat with **8532**: |
| 54 | + |
| 55 | +* **Step 2:** Largest number: 8532 |
| 56 | +* **Step 3:** Smallest number: 2358 |
| 57 | +* **Step 4:** Subtract: 8532 - 2358 = **6174** |
| 58 | + |
| 59 | +Again, we arrived at 6174! |
| 60 | + |
| 61 | +## The Magic of 6174 |
| 62 | + |
| 63 | +This number, 6174, is known as **Kaprekar's Constant**. For almost any four-digit number (with at least two different digits), if you keep applying Kaprekar's routine, you will eventually reach 6174. Once you reach 6174, the next step will always be: |
| 64 | + |
| 65 | +* Largest: 7641 |
| 66 | +* Smallest: 1467 |
| 67 | +* Subtract: 7641 - 1467 = **6174** |
| 68 | + |
| 69 | +It's a loop! |
| 70 | + |
| 71 | +Kaprekar's routine is a wonderful example of how simple arithmetic operations can lead to unexpected and beautiful mathematical constants. Try it with your own four-digit numbers and see the magic unfold! |
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