A and B are two numbers. The non-zero digit in the crore's place of A is 3 less than the digit in the hundreds place of B. The non-zero digit in 10's place of B is 2 less than the number in 10's place of A. If both the numbers have equal number of digits and all the remaining digits are equal but not zeros, then find the least possible difference between A and B.

Explanation

To solve the problem step by step, let's break down the information given and find the least possible difference between the two numbers A and B.

### Step 1: Understand the conditions
We have two numbers A and B with the following conditions:
1. The non-zero digit in the crore's place of A is 3 less than the digit in the hundreds place of B.
2. The non-zero digit in the tens place of B is 2 less than the digit in the tens place of A.
3. Both numbers have an equal number of digits, and all remaining digits are equal but not zeros.

### Step 2: Assign variables
Let's denote:
- The digit in the crore's place of A as \( a \).
- The digit in the hundreds place of B as \( b \).
- The digit in the tens place of A as \( x \).
- The digit in the tens place of B as \( y \).

From the conditions, we can write:
- \( a = b - 3 \)
- \( y = x - 2 \)

### Step 3: Choose values for \( a \) and \( b \)
Since \( a \) and \( b \) are digits (1 to 9), we can start by selecting the smallest possible values:
- Let’s choose \( a = 1 \). Then, from \( a = b - 3 \), we have:
\[ 1 = b - 3 \implies b = 4 \]

### Step 4: Choose values for \( x \) and \( y \)
Next, we will choose values for \( x \) and \( y \):
- Let’s choose \( x = 3 \). Then, from \( y = x - 2 \), we have:
\[ y = 3 - 2 = 1 \]

### Step 5: Construct the numbers A and B
Now we can construct the numbers A and B:
- A will have the crore's place as \( a = 1 \), the hundreds place as \( 4 \), and the tens place as \( 3 \). We can fill the remaining digits with the same non-zero digit, say \( 1 \):
\[ A = 1, 1, 1, 1, 4, 3 \]
So, \( A = 1,11,11,413 \).

- B will have the crore's place as \( 4 \), the hundreds place as \( 4 \), and the tens place as \( 1 \). Again, we can fill the remaining digits with the same non-zero digit, say \( 1 \):
\[ B = 1, 1, 1, 1, 4, 1 \]
So, \( B = 1,11,11,141 \).

### Step 6: Calculate the difference
Now we calculate the difference between A and B:
\[ \text{Difference} = A - B = 1,11,11,413 - 1,11,11,141 \]
Calculating this gives:
\[ 1,11,11,413 - 1,11,11,141 = 272 \]

### Conclusion
The least possible difference between A and B is **272**.