Difference between revisions of "1997 PMWC Problems/Problem T5"

(See also)
Line 21: Line 21:
==See also==
==See also==
{{PMWC box|year=1997|num-b=T4|num-a=T6}}
{{PMWC box|year=1997|num-b=T4|num-a=T6}}
[[Category:Logic Problems]]

Revision as of 10:28, 24 August 2008


During recess, one of five pupils wrote something nasty on the chalkboard. When questioned by the class teacher, the following ensued:

'A': It was 'B' or 'C'

'B': Neither 'E' nor I did it.

'C': You are both lying.

'D': No, either A or B is telling the truth.

'E': No, 'D', that's not true.

The class teacher knows that three of them never lie while the other two cannot be trusted. Who was the culprit?


Case 1: A is telling the truth

Thus it was either B or C. Since A is telling the truth, C is lying. If D is telling the truth, then B is lying, and E is lying, but that's impossible. Thus D is lying. Then E is telling the truth, and so is B. Thus two people are lying (C and D), and the other three are telling the truth. Since it was one of B or C, and it wasn't B, it must have been C.

See also

1997 PMWC (Problems)
Preceded by
Problem T4
Followed by
Problem T6
I: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T: 1 2 3 4 5 6 7 8 9 10
Invalid username
Login to AoPS