Let A, B and C represent distinct non-zero digits. Suppose x is the sum of all possible 3-digit numbers formed by A, B and C without repetition. Consider the following statements:<br/>1. The 4-digit least value of x is 1332.<br/>2. The 3-digit greatest value of x is 888.<br/><br/>Which of the above statements is/are correct?

For distinct non-zero digits (A,B,C), the sum of all 3-digit numbers formed without repetition is (x=2\times111\times(A+B+C)=222(A+B+C)).

Statement 1: The least 4-digit value of (x) occurs at the smallest possible (A+B+C) with distinct non-zero digits, i.e. (1+2+3=6). Hence (x=222\times6=1332). Verdict: Correct.

Statement 2: My earlier conclusion was mistaken. Interpreting the statement as asking for the greatest 3-digit number that can be written in the form using digits (A,B,C), the maximum is (888). But this does not fit the condition of three distinct non-zero digits used without repetition in forming the numbers, so the statement is not valid in the given setup. Verdict: Incorrect.

Hence only Statement 1 is correct. Disclaimer: The direct formula shows (x) itself can never be 3-digit for distinct non-zero digits, which also makes Statement 2 false.