Question

E-1, E-2 and E-3 are three engineering students writing their assignments at night. Each of them starts at a different time and completes at a different time. The digit in their name and the order of their starting and completing the assignment is certainly not the same. The last student to start is the first to complete the assignment.
Who is the last student to complete the assignment?

• A. E-1
• B. E-2
• C. E-3
• D. Cannot be decided

Hint:

First work out the starting order and who finishes first, then the last two completion slots follow by elimination.

Answer 1

The Correct Option is A

We can also find the answer by directly testing each student as the "last to complete" candidate and checking for contradictions with the puzzle's rules.

1. Rule recap: no student's starting or completion position can match their own name digit, and whichever student starts last must be the one who finishes first.
2. Test E-2 as last to complete: this would mean C(E2) = 3. E-2's own digit is 2, so this does not break the naming rule by itself. But from the starting-order analysis, E-2 is the last to start, so E-2 must actually be first to complete, meaning C(E2) = 1, not 3. This is a direct contradiction, so E-2 cannot be last to complete.
3. Test E-3 as last to complete: this would mean C(E3) = 3, but E-3's own name digit is 3, so this directly violates the rule that a completion position cannot equal the student's own digit. So E-3 cannot be last to complete.
4. Test E-1 as last to complete: this would mean C(E1) = 3. E-1's own digit is 1, and 3 does not equal 1, so this does not break the naming rule. Checking the rest: E-2 is first to complete (from the starting-order deduction), and the only remaining position, 2, must go to E-3, giving C(E3) = 2, which does not equal 3, so this is valid with no contradictions.

Since testing E-2 and E-3 as last to complete both lead to contradictions, and only E-1 works without contradiction, E-1 is the last student to complete the assignment, confirming option (1) as the correct answer.