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Hi Puzzling Stack Exchange! Here's a quick deduction puzzle I thought of. It's a slight twist on the classic version, but should prove fun (not agonising) to solve. Enjoy!

sound of breaking glass

Those moronic kids. Looking out your window, you can see a boy run away from your house; however, the frost on the glass blurred out any defining features.

You make your way downstairs. The cracking of your legs is almost as loud as the creaking of the dusty, wooden staircase.

As you reach the bottom, you almost drop your walking stick in horror.

The family heirloom: a vase, made from the finest china, and passed down from generation to generation for over five hundred years, lay on the floor, shattered into pieces. Next to it was a stone - the obvious destroyer.

Luckily for you, you live in a very small town. There are seven male kids in your town: Arthur, Benjamin, Connor, Daniel, Eric, Frederick, and Gary. You ask them to each tell you one thing, and to make this riddle more easily solvable, you know for a fact that three of them will definitely give you (and each other) falsified information, whereas the other four will definitely give you (and each other) truthful information.

Arthur: I think that Daniel thinks that Eric will tell the truth.

Benjamin: I know Gary, and I know for a fact that Gary and I will both tell the truth.

Connor: I don't know who threw the stone, but it was either Daniel, Eric, or Frederick.

Daniel: I know both Connor and Eric, and I know for a fact that they will either both lie, or both tell the truth.

Eric: I don't know who threw the stone, but it was either Benjamin, Connor, or Daniel.

Frederick: I think that Gary thinks that Connor thinks that Arthur will lie.

Gary: I know both Arthur and Benjamin, and I know for a fact that one of them is a liar, and one of them will tell the truth.

Hmm. Perhaps it would have been easier if you had asked them questions instead.

Who threw the stone?

Note: Just to make the above information a little clearer so there are no misconceptions, if someone is a liar, they will lie to the other kids as well! For example:

Larry is a liar. Martin is a liar.

If you ask Larry what he thinks of Martin, he will say that Martin is a liar. This is because Martin would tell Larry that he tells the truth, but Larry would lie to you, telling you that Martin is a liar.

However, if Larry says that he knows Martin, he will tell you that he knows for a fact that Martin will tell the truth. This is because he knows Martin is a liar, and will lie to you, telling you that Martin will tell the truth.

Update: Can't believe I didn't include this, but it was a liar that threw the stone. Hopefully that should help clear things up.

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  • $\begingroup$ Your last few paragraphs aren’t exceedingly clear.  First of all, anybody who either tells the truth consistently or lies consistently will claim to be honest.  So, how well do the boys know each other?  If Sam says that he thinks that Tom thinks (something), is Sam relaying (possibly an inverted version of) what Tom has said, or does Sam have some reliable way of knowing what Tom thinks (about which Sam might lie)?  If Sam says he knows Tom, but Sam is a liar, that means that Sam doesn’t  know Tom, so how should we interpret the statement that Sam says he “knows for a fact”? $\endgroup$
    – Peregrine Rook
    Jul 15, 2017 at 5:59
  • $\begingroup$ @PeregrineRook Assuming Gary is not a liar, since Gary says he knows both Arthur and Benjamin, then he will know for a fact that one of them is a liar, and one of them will tell the truth. Obviously if you ask either Arthur or Benjamin, both of them will tell you that they are truthful. In the event that Gary is a liar, obviously none of this would matter. Are there any further misconceptions you wish for me to clear up? $\endgroup$
    – Lucas
    Jul 15, 2017 at 6:14
  • $\begingroup$ @PeregrineRook Sam would have observed Tom lying, instead of relying on what he claims to be $\endgroup$
    – micsthepick
    Jul 15, 2017 at 7:49

2 Answers 2

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My answer, although this question does not seem to be 100% solid in it's logic:

If you are a liar, and you are asked if you tell the truth, you will answer the same as if you were not a liar, claiming to be a truth teller. I thought that this means either out of Arthur and Daniel either both lie or both tell the truth, as Daniel would think that Eric will tell the truth either way, and either Daniel lies to Arthur who lies to us to get that statement, or they both tell the truth. This logic is flawed, as Daniel knows Eric, But the case where both are liars still works.

if both are lying, then between Connor and Eric, there is one truth-teller and one liar, both cannot be the same, or Daniel is not a liar, and that gives three liars, so everyone else is a truth teller, by what Frederick says, Connor must be a liar, and therefore Eric tells the Truth, so It cannot be Daniel who threw the stone, it must be Connor who threw the stone as Benjamin tells the truth.

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  • $\begingroup$ Oh darn, I misworded the question - I'm really sorry. Please refer to my edit. $\endgroup$
    – Lucas
    Jul 14, 2017 at 22:58
  • $\begingroup$ Yes, this changes things $\endgroup$
    – micsthepick
    Jul 14, 2017 at 23:00
  • $\begingroup$ @think123 does Daniel know Connor and Eric, or is he basing his statement on what he is told by them? $\endgroup$
    – micsthepick
    Jul 14, 2017 at 23:05
  • $\begingroup$ Check my edit. I really need some sleep. $\endgroup$
    – Lucas
    Jul 14, 2017 at 23:11
  • $\begingroup$ @think123 In total, It could have been any one out of four individuals with this information I believe $\endgroup$
    – micsthepick
    Jul 15, 2017 at 4:56
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The statements lead me to two possible answers:

Arthur, Eric and Daniel are the liars; any other answer creates paradoxes, so since Connor says the truth, we know that can not be Daniel since Eric is lying. Then it could be Frederick or Eric, (the fact that one of them is lying does not imply that was the one who threw the stone).

so I may be wrong.

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  • $\begingroup$ I think you are wrong because of what Frederick says, By what he says, between him Gary and Connor either on or all must be liars, otherwise the statement would be that Arthur will tell the truth. $\endgroup$
    – micsthepick
    Jul 15, 2017 at 5:01
  • $\begingroup$ * either one or all (of Fredrick Gary and Connor are liars) $\endgroup$
    – micsthepick
    Jul 15, 2017 at 7:45

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