IMC 2010 Q11
11. “You eat more than I do,” said Tweedledee to Tweedledum.
“That is not true,” said Tweedledum to Tweedledee.
“You are both wrong,” said Alice, to them both.
“You are right,” said the White Rabbit to Alice.
How many of the four statements were true?
- A 0
- B 1
- C 2
- D 3
- E 4
Intermediate Mathematical Challenge 2010, Question 11. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 1
If the first statement is true, then the three other statements are all false. If the first statement is false, however, then the second statement is the only true statement. Either way, exactly one of the four statements is true.
Solution © UK Mathematics Trust, from the IMC 2010 solutions.