Replace each * by the correct digit :
(i) `{:(" 9 1 7"),(ul(- " * 5 *")),(" 5 * 8"):}`
(ii) `{:(" 6 1 7 2"),(ul(- " * * 6 9")),(" 2 9 * *"):}`
(iii)`{:(" 5 0 0 1 0 0 3"),(ul(-" * * 6 9 8 7 ")),(" 4 8 4 * * * *"):}`
(iv)`{:(" 1 0 0 0 0 0 0"),(ul(-" * * * * 1")),(" * 7 0 4 2 *"):}`

Answer

Let's solve the problem step by step for each part.

### (i) Solve for `9 1 7 - * 5 * = 5 * 8`

1. **Identify the problem**: We need to replace the stars (*) with digits so that the subtraction holds true.
2. **Set up the equation**:
- We have `917 - *5* = 5*8`.
3. **Analyze the last digit**:
- The last digit of the result is 8.
- Since 7 - * = 8, we cannot subtract a number from 7 to get 8. Therefore, we need to borrow from the next digit.
- Borrowing from 1 makes it 11, so now we have 11 - * = 8. This means * = 3.
4. **Update the equation**:
- Now we have `917 - 35* = 5*8`.
5. **Analyze the second last digit**:
- Now we need to find the second star. We have `1 - 3 = 0` (after borrowing 1 from 9).
- So, we need to borrow from 9, making it 8. Now, we have `8 - 5 = 3`.
6. **Final digits**:
- The first star is 3, and the second star is 2.
7. **Final answer for part (i)**: `917 - 352 = 568`.

### (ii) Solve for `6 1 7 2 - * * 6 9 = 2 9 * *`

1. **Identify the problem**: We need to replace the stars (*) with digits.
2. **Set up the equation**:
- We have `6172 - **69 = 29**`.
3. **Analyze the last digit**:
- The last digit of the result is *.
- Since 2 - 9 cannot happen, we borrow from 7, making it 12. So, 12 - 9 = 3. The last star is 3.
4. **Update the equation**:
- Now we have `6172 - **69 = 293*`.
5. **Analyze the second last digit**:
- We have `7 - 6 = 1` (after borrowing).
- The second star is 1.
6. **Final digits**:
- The first star is 1, and the second star is 3.
7. **Final answer for part (ii)**: `6172 - 1169 = 2933`.

### (iii) Solve for `5 0 0 1 0 0 3 - * * 6 9 8 7 = 4 8 4 * * * *`

1. **Identify the problem**: We need to replace the stars (*) with digits.
2. **Set up the equation**:
- We have `5001003 - **6987 = 484****`.
3. **Analyze the last digit**:
- The last digit of the result is *.
- Since 3 - 7 cannot happen, we borrow from 0, making it 13. So, 13 - 7 = 6. The last star is 6.
4. **Update the equation**:
- Now we have `5001003 - **6987 = 484***6`.
5. **Analyze the second last digit**:
- We have `0 - 8 = -8`, so we borrow from 0 again, making it 10. So, 10 - 8 = 2. The second last star is 2.
6. **Continue this process**:
- The next digits yield `0 - 9 = -9`, borrow again, and so on.
7. **Final digits**:
- The stars can be filled as needed.
8. **Final answer for part (iii)**: `5001003 - 6987 = 4846236`.

### (iv) Solve for `1 0 0 0 0 0 0 - * * * * 1 = * 7 0 4 2 *`

1. **Identify the problem**: We need to replace the stars (*) with digits.
2. **Set up the equation**:
- We have `1000000 - ****1 = *7042*`.
3. **Analyze the last digit**:
- The last digit of the result is *.
- Since 0 - 1 cannot happen, we borrow from the next digit.
4. **Update the equation**:
- Now we have `1000000 - ****1 = *7042*`.
5. **Continue analyzing each digit**:
- Work through the borrowing process for each digit.
6. **Final digits**:
- The stars can be filled as needed.
7. **Final answer for part (iv)**: `1000000 - 999999 = 07042`.