There is something very special about the number 6174. Select any four-digit number whose digits are not equal, and arrange the digits to form the largest possible number, that is, put the digits in decreasing order from left to right. Then form the reverse of this number and subtract it from the larger number. Continue this process by forming the largest possible number from the difference and subtracting the reverse. The example in the following table shows the process ending with 6174 after five steps.

Step Maximun Number Reverse Difference

1 8421 1248 7173

2 7731 1377 6354

3 6543 3456 3087

4 8730 0378 8352

5 8532 2358 6174

1. If you begin with any four-digit number whose digits are not all equal, will the above process always product 6174?

2. What happens when this process is applied to three-digit numbers whose digits are not all equal? Is there a special number in this case?

3. What happens when the process is applied to five-digit numbers? Is there a special number in this case?

4. You may wish to continue this investigation for numbers with more digits.

1.

Step Maximun Number Reverse Difference

1. 8721 1278 7443

2. 7443 3477 3996

3. 9963 3699 6264

4. 6642 2466 4176

5. 7641 1467 6174

Step Maximun Number Reverse Difference

1. 5432 2345 3087

2. 8730 0378 8352

3. 8532 2358 6174

2.

Step Maximun Number Reverse Difference

1. 210 012 198

2. 981 189 792

3. 972 279 693

4. 963 369 594

5. 954 459 495

Step Maximun Number Reverse Difference

1. 654 456 198

2. 981 189 792

3. 972 279 693

4. 963 369 594

5. 954 459 495

Step Maximum Number

Reverse Difference

1. 84321 12348 71973

2. 97731 13779 83952

3. 98532 23589 74943

4. 97443 34479 62962

5. 96624 24669 71955

6. 97551 15579 81972

7. 98721 12789 85932

3.

Step Maximum Number

Reverse Difference

1. 87651 15678 71973

2. 97731 13779 83952

3. 98532 23589 74943

4. 97443 34479 62964

5. 96624 24469 71955

6. 97551 15579 81972

7. 98721 12789 85932

Prepared by:Lyra R. PolinaresSubmitted to:Prof.Editha Magsino