Math Kangaroo’s Logic Puzzle
My AMSA students loved the following puzzle from the 2003 Math Kangaroo contest for grades 7-8:
Share:The children A, B, C and D made the following assertions.
- A: B, C and D are girls.
- B: A, C and D are boys.
- C: A and B are lying.
- D: A, B and C are telling the truth.
How many of the children were telling the truth?
A) 0 B) 1 C) 2 D) 3 E) Impossible to determine
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Leo:
Were any of the children transgendered?
22 May 2014, 2:02 pmanon:
D is clearly lying. One or both of A and B are lying. If both A and B are lying, then C is telling the truth. If one of A and B is lying, then C is lying. Either way one person is telling the truth.
23 May 2014, 2:34 pmDouglas J. Keenan:
The sought-for answer is, presumably, 1, but that is incorrect. As worded, either 1 or 0 people could be telling the truth; hence the correct answer is “Impossible to determine”.
The difficulty here is that someone might not be lying but could still be wrong. For example, both A and B could be wrong, but honestly mistaken; thus neither is lying, and so C is wrong too. In this example, then, there are 0 people telling the truth.
Perhaps the third assertion should be reworded, e.g. “Neither A nor B is telling the truth”.
5 June 2014, 2:18 pmLori:
Wow, this question seems a bit confusing for a middle schooler. We’ve tried out Math Kangaroo before but it didn’t work out as much as we had hoped. Beestar has been a pretty good option with their online competitions.
4 October 2021, 10:10 pm