Answer: We discover two outcomes:
1000 - 998 = 2
1001 - 999 = 2
Step-by-step explanation:
The problem can be stated as:
****-*** = 2
Where each asterisk symbolizes a distinct digit; here with a 4-digit number subtracting a 3-digit number to yield a difference of 2.
This can be represented as 99*, where we can increase any digit from 1 to 9 and we will achieve a 4-digit result:
So we rewrite it this way:
1000 - 998 = 2
When we add one to each side, the difference remains preserved, maintaining equal digit counts:[
1000 - 998 + 1 - 1 = 2
(1000 + 1) - (998 + 1) = 2
Thus, 1001 - 999 = 2
A simple case would also yield further solutions where digits can be zeros, for instance:
0004 - 0002 = 2
However, this trivial solution may be disregarded. This leads us to conclude that we have two unique solutions.
Response:
I am uncertain.
Step-by-step clarification:
