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Three friends are playing a game of memory, there are a total of 20 cards with 10 card pairs. They try to make the most pairs in a row, after everyone had a turn they make the following statements:

Person a: "I've made 10 pairs in a row, I'm perfect".

Person b: "I've made 9 pairs in a row, I'm not the best but I'm good enough".

Person c: "I've made 5 pairs in a row, I could do worse".

One person is lying, who is it?

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  • $\begingroup$ This problem isn't very clear what they are doing? Is there a procedure for playing this memory game? $\endgroup$ – LeppyR64 May 27 '15 at 9:55
  • $\begingroup$ This problem isn't very clear what they are doing? Is there a procedure for playing this memory game? $\endgroup$ – LeppyR64 May 27 '15 at 9:59
  • $\begingroup$ They are just playing memory (never played it I guess?), they are trying to make the most pairs in a row individually, after person a tried to make the most pairs in a row, it's person b's turn. Is it really that difficult? $\endgroup$ – Wouter May 27 '15 at 10:01
  • $\begingroup$ So A pulls cards off the deck until they get a miss and then they reset the deck for B? $\endgroup$ – LeppyR64 May 27 '15 at 10:04
  • $\begingroup$ en.wikipedia.org/wiki/Concentration_%28game%29 look there for more information about the game: memory $\endgroup$ – Wouter May 27 '15 at 10:06
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well,

9 pair in a row is not possible .. because the two last (or first) cards have to be a pair as well (only a pair left), thus making it 10 pairs in a row .. so, B is lying.

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  • $\begingroup$ This might be me misunderstanding the question, but if he picked the last pair as first and last card he would get 9 pairs in a row. $\endgroup$ – Ciacciu May 27 '15 at 9:28
  • $\begingroup$ well, I could have misunderstood the question, as well, but .. I tought that players where removing two cards from the twenty, 10 times, trying to match pairs. If the card are removed, obviously, 9 in a row is the only impossible configuration. $\endgroup$ – Den May 27 '15 at 9:33
  • $\begingroup$ It's a perfectly fine assumption, I believe :) $\endgroup$ – Ciacciu May 27 '15 at 9:39
  • $\begingroup$ You were right @Den It's just like a game of memory, got a pair, continue, no pair game over. $\endgroup$ – Wouter May 28 '15 at 7:33
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The answer is

Person B. If he got 9 pairs, there's only two matched cards left, meaning he's actually gotten all 10 pairs.

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Either B or C, but it's impossible to know, if we assume that "I could do worse" means "someone did worse than me". B if "I could do worse" means "I didn't get the worst theoretical possible"

  1. Let's assume A is lying and B and C are telling the truth. B states that he is not the best, which would mean he's lying, so without going further we can tell that A is telling the truth.

  2. Let's assume B is lying. A's assertion doesn't conflict with B's, and if B did indeed make less that 5 pairs in a row, that would mean C is telling the truth.

  3. Let's assume C is lying. With the above assumption he could be lying, and indeed be the one who did worst.

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