A Conundrum To Ponder
So back in the grammar school days I was entered into the Maths Challenges, a competition for budding young mathematicians. Those who passed the grade were selected for national finals and then have the opportunity to represent the UK internationally. So a friend of mine; Sam, reminded me of this as he's been having a boring time at work so he googled a question he remembered and proceeded to spend the rest of the day answering past paper questions. So I challenge you do get your logic head on and figure this one out:
By the way I can't figure this one out so if you can leave a comment with the answer. Also if you're still bored get more questions (of a more mathsy nature) here and/or here.
The Queen of Hearts had some tarts, but they were eaten. Precisely one of the following statements about the tarts and the Knaves of Clubs, Diamonds and Spades is true. Which one?Hint: use the fact that one and only one of the statements is true.
- None of the three Knaves ate any tarts,
- the Knave of Clubs ate some tarts,
- only one of the three Knaves ate any tarts,
- at least one of the Knave of Diamonds and the Knave of Spades ate no tarts,
- more than one of the three Knaves ate some tarts.
By the way I can't figure this one out so if you can leave a comment with the answer. Also if you're still bored get more questions (of a more mathsy nature) here and/or here.
posted by Simon @ 6:22 PM
8 comments
8 Comments:
The answer is A. none of the Knaves either clubs diamonds or spades ate them, because it was the Knave of Hearts that took them clean away. De derrrrrr :-)
Steph
The opening statement (about the queen and some tarts) is a bit of a distraction here. If one and only one of the statements is true then by a process of elimination (proof by contradiction?!) only one of those statements can be true. In all other cases, a least two of the statements will be true, which isn't the case, you see? Something like that . . . I know what I'm talking about anyway.
Damn it - I posted a comment with (kind of) the answer, but it's gone. Grrrr. Anyway, the bit about the Queen of Hearts and some tarts is a bit of distraction here. See, if statement (a) is true, that none of the knaves ate any of the tarts, then also statement (d) is true, because both the knave of diamonds and the knave of spades will have eaten no tarts. If statement (b) is true, that the knave of clubs ate some tarts, then either statement (c) is true or else statement (e) is true, depending on whether the knave of clubs ate alone or not. If statement (e) is true, that more than one of the knaves ate some tarts, then all the other statements are false (if we assume that the knaves who ate some tarts were the diamonds and the spades). This may or may not be something to do with proof by contradiction.
Jonath, I like your thinking, however surely if (e) is true then so can be (d) can't it?
Any more answers?
Indeed. However, if we assume that the knaves who ate some tarts were the diamonds and the spades, then the only true statement is (e) - all others are false. It is possible for statement (e) to be true and other statements to be true, if other combinations of knaves ate some tarts.
Aha! Then we should consider all 8 possibilities!
1. Clubs ate them,
2. Diamonds ate them,
3. Spades ate them,
4. Clubs and Diamonds ate them,
5. Clubs and Spades ate 'em,
6. Diamonds and Spades ate 'em,
7. All three ate 'em
8. None ate them.
only one of those 8 statements is true as they are mutually exclusive. Does that work?
Exactly! I think we've cracked it then. Next puzzle, please.
Jonath, as much as I'd like to post some more problems the majority of them are fairly in depth mathematically speaking. Click the links at the bottom of the post for infinitely more note ∞≈50
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