Find value of A & B:
`{:("A B"),("x 6"),(---),("B B B"),(---):}`

Answer

To solve the problem of finding the values of A and B in the equation \( AB \times 6 = BBB \), we will follow these steps:

### Step 1: Understand the equation
The equation \( AB \times 6 = BBB \) means that when we multiply the two-digit number \( AB \) (where A is the tens place and B is the units place) by 6, we should get a three-digit number where all digits are the same (i.e., \( BBB \)).

### Step 2: Identify the possible values of B
Since \( BBB \) is a three-digit number with all the same digits, the possible values for B (the unit digit) can be 0, 2, 4, 6, or 8. This is because these are the digits that, when multiplied by 6, will still end with the same digit.

### Step 3: Check each possible value of B
1. **If B = 0**:
- \( AB = A0 \)
- \( A0 \times 6 = 000 \) (not valid since it doesn't give a three-digit number).

2. **If B = 1**:
- \( A1 \times 6 = 111 \) (not valid since \( 1 \times 6 = 6 \)).

3. **If B = 2**:
- \( A2 \times 6 = 222 \)
- Dividing \( 222 \) by \( 6 \):
\[ 222 \div 6 = 37 \]
- This gives \( A = 3 \) (not valid since 3 is not a single digit).

4. **If B = 3**:
- \( A3 \times 6 = 333 \) (not valid since \( 3 \times 6 = 18 \)).

5. **If B = 4**:
- \( A4 \times 6 = 444 \)
- Dividing \( 444 \) by \( 6 \):
\[ 444 \div 6 = 74 \]
- This gives \( A = 7 \).

6. **If B = 5**:
- \( A5 \times 6 = 555 \) (not valid since \( 5 \times 6 = 30 \)).

7. **If B = 6**:
- \( A6 \times 6 = 666 \) (not valid since \( 6 \times 6 = 36 \)).

8. **If B = 7**:
- \( A7 \times 6 = 777 \) (not valid since \( 7 \times 6 = 42 \)).

9. **If B = 8**:
- \( A8 \times 6 = 888 \)
- Dividing \( 888 \) by \( 6 \):
\[ 888 \div 6 = 148 \]
- This gives \( A = 14 \) (not valid since 14 is not a single digit).

### Step 4: Conclusion
From the above checks, the only valid values we found are:
- \( A = 7 \)
- \( B = 4 \)

Thus, the values of A and B are:
\[ \text{A} = 7, \text{B} = 4 \]