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Logic Level 3

There are three brothers: John, Mark, Kane. One day, their mom made a cake. However, a slice of the cake went missing. The boys made the following statements:

John said, "Mark didn't eat it."
Mark said, "Kane ate it."
Kane said, "Mark ate it."

If two of them lied and one of them told the truth, then who took the slice of cake?

Kane Not enough information John Mark

5 solutions

Last Sword
Jul 9, 2015

John and mark can eat it, not enough information.

At first, it looks like there isn't enough information, since John telling the truth implies that he ate the cake and Kane telling the truth implies that Mark ate the cake (the third case leading to a contradiction). But If you also assume that the one who ate the cake is more likely to lie to protect himself, then Kane is telling the truth and Mark ate the cake. Here's a more convincing argument: since these are all witnesses and know the answer, it makes more sense for Kane to accuse Mark, who really ate the cake, and for John, presumably on Mark's side, to try to put the blame off Mark while Mark accuses Kane. If John is telling the truth and ate the cake, then Mark and Kane are accusing each other while knowing John ate the cake and John, instead of accusing someone else, bizarrely chooses to put the blame off someone he knows didn't eat the cake. You could try to justify this behaviour by assuming that two people must be teaming up against the third, but for any pair of friends you choose, you still get bizarre behaviours because either Mark or Kane must in any case be against John, in which case it would make more sense for at least one of them to accuse John, which neither does. In conclusion, Kane is telling the truth and Mark ate the cake and the person who put that problem set the wrong answer >:-(

Sébastien Laberge - 5 years, 11 months ago

It's a logic problem, not child psychology. Get over it. The correct answer is 'not enough info'.

Steven Bukoan - 5 years, 11 months ago

Motive is irrelevant. "More likely" means nothing.

Either a situation fits the description or it doesn't.

Without additional information other than what is presented without ASSUMING anything, you can't answer the question.

Case 1: John eats the cake. John is telling the truth, because Mark did NOT eat the cake. Mark is lying, because Kane did NOT eat the cake. Kane is lying, because Mark did NOT eat the cake.

Case 2: Mark eats the cake. John is lying, because Mark DID eat the cake. Mark is lying, because Kane did NOT eat the cake. Kane is telling the truth, because Mark DID eat the cake.

Based on the information given, each case is equally possible.

Matt Steele - 5 years, 8 months ago

How about the case when John has eaten the cake and Kane and Mark had a fight the previous day. As soon as a piece was found missing they just blame eaxh other. What if John is a nice guy who does not want Mark to be blamed for his mistake and ant the same time does not want to give himself away. So he just says Mark didnt eat it!!!

Anand Santhanakrishnan - 5 years, 8 months ago

While the refutations here are more than sufficient, they barely scratch the surface of the flaws in the analysis.

In short, you assume a GREAT DEAL of facts NOT in evidence--for starters, assuming John, Mark and Kane (& their mother) are human / have human motivations to begin with. This (along with a great deal more) is not in evidence and should never be automatically assumed...

Joshua Nesseth - 4 years, 5 months ago

Yes. Mark ate it and I got it wrong though I know I am right.

Jaymund Ostonal - 5 years, 11 months ago

John could have eaten it too. In that case, Mark and Kane would both be lying but John would be telling the truth. Therefore, there are two correct answers, and thus not enough information to find just one solution.

Rocco Tenaglia - 5 years, 11 months ago

same, i know i am right

uttkarsh kohli - 5 years, 11 months ago

i also give the right answer mark even then it was wrong why??

Mohit Bhargava - 5 years, 11 months ago

@Mohit Bhargava – same here :(

Hasan Ali - 5 years, 11 months ago

Awesome analysis, sir

Flávio Gomes - 5 years, 8 months ago

Not from a logic standpoint.

Matt Steele - 5 years, 8 months ago

I deduced the same... Mark was my choice..

Tanmoy Gupta - 5 years, 9 months ago

Yes the condition that only one is telling truth fails if the answer is "Not Enough Information". So Mark ate the Cake and Kane speaks the truth. John and Mark are liars.

Joe Nithin - 5 years, 8 months ago

I agree ..problem setter sets wrong option and!! Mark ate it is right

Akshay Baviskar - 5 years, 11 months ago

if john's statement is true then john ate it,if kane statement is true mark ate it so the answer is not enough information

uttkarsh kohli - 5 years, 11 months ago

John's statement can't be true because it gives us 2 options as an answer (both John and Kane) John's statement does not specifies that Kane did not eat the cake and does not give us any idea about 2nd true statement

PS Prateek - 5 years, 11 months ago

Since when does a true statement have to be specific?

Nate Thönnesen - 5 years, 8 months ago

look at the question

uttkarsh kohli - 5 years, 11 months ago

Let's say 3rd statement is true and rest is false... Explain now

Tanmoy Gupta - 5 years, 9 months ago

I have no idea about this. Why Mark is wrong???

Supakit Kuewsupakorn - 5 years, 8 months ago

It would have been better if it could be shown John did eat it--then, despite being the culprit, he is still the only one of the three that didn't lie AND is the only one who didn't try to sell out another one of his brothers (despite having the most to gain...).

Joshua Nesseth - 4 years, 5 months ago

i think information can be considered enough as it is written that there are two lies than 1st and 2nd statement are lies and third one is correct.as a/c to my answer mark ate it so 1st and 2nd is lie.

Ayush Krishna - 5 years, 8 months ago

Agree. Mark could have eaten it, but if John ate it: - John is telling the truth. - Mark is lying. - Kane is lying.

So it could have been John too.

There's not enough info. The accepted answer seems wrong to me.

Norm Nolasco - 5 years, 11 months ago

if u agree u should upvote it

uttkarsh kohli - 5 years, 11 months ago

If John is saying the truth then Mark is also telling the truth, and since the question itself says that there are 2 lies and only 1 true statement then only the third statement can be true for the given conditions (as in the question) This proves that Kane is telling the truth which in turn gives us the answer that Mark ate the piece of cake

PS Prateek - 5 years, 11 months ago

Uttkarsh Kohli
Aug 14, 2015

not enough info ...................................

Ahmed Obaiedallah
Jul 21, 2015

John an Mark, so it's not enough info

Joel Icon
Jul 10, 2015

Logically, I'd assume Kane ate the cake, as John absolved Mark and Mark accused Kane. More pointers at Kane, than Mark or John...The original answer still follows, but I'd put my money on Kane if it was my cake! :))

John Ramos
Jul 10, 2015

Either John or Mark took the missing slice of cake. Not enough information.

i disagree, Mark ate the cake. because stipulation states that 2 of them lied. hence, John lied when he told his mother that Mark didn't eat the cake and so is Mark when he told his Mother that Kane ate the cake. Hence, Mark is the rightful answer.

John Rick Hugo - 5 years, 11 months ago

If John ate the cake, he is the only one telling the truth ("Mark didn't eat the cake.").

So you're wrong.

Matt Steele - 5 years, 8 months ago

Damn didnt think of that, gg

Simon Fisher - 5 years, 9 months ago

Try your luck

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