# Who is the liar?

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?

• This problem isn't very clear what they are doing? Is there a procedure for playing this memory game? May 27, 2015 at 9:55
• This problem isn't very clear what they are doing? Is there a procedure for playing this memory game? May 27, 2015 at 9:59
• 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? May 27, 2015 at 10:01
• So A pulls cards off the deck until they get a miss and then they reset the deck for B? May 27, 2015 at 10:04

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.

• 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. May 27, 2015 at 9:28
• 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.
– Den
May 27, 2015 at 9:33
• It's a perfectly fine assumption, I believe :) May 27, 2015 at 9:39
• You were right @Den It's just like a game of memory, got a pair, continue, no pair game over. May 28, 2015 at 7:33