Streeeetch Your Mind!
LOGIC PROBLEMS
Pandora’s Box I
Once upon a time, there was a girl named Pandora, who wanted a bright groom so she made up a few logic problems for the wannabe. This is one of them.
Based upon the inscriptions on the boxes (none or just one of them is true), choose one box where the wedding ring is hidden.
Golden box
The ring is in this box.
Silver box
The ring is not in this box.
Lead box
The ring is not in the golden box.
Pandora’s Box II
And here is the second test. At least one inscription is true and at least one is false. Which means the ring is in the...
Golden box
The ring is not in the silver box.
Silver box
The ring is not in this box.
Lead box
The ring is in this box.
Lion and Unicorn
Alice came across a lion and a unicorn in a forest of forgetfulness. Those two are strange beings. The lion lies every Monday, Tuesday and Wednesday and the other days he speaks the truth. The unicorn lies on Thursdays, Fridays and Saturdays, however the other days of the week he speaks the truth.
Lion: Yesterday I was lying.
Unicorn: So was I.
Which day did they say that?
Island Baal
There are people and strange monkeys on this island, and you can not tell who is who. They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.
Truth, Lie and Wisdom
Three goddesses were sitting in an old Indian temple. Their names were Truth (always telling the truth), Lie (always lying) and Wisdom (sometimes lying). A visitor asked the one on the left: “Who is sitting next to you?”
“Truth,” she answered.
Then he asked the one in the middle: “Who are you?”
“Wisdom.”
Lastly, he asked the one on the right: “Who is your neighbor?”
“Lie,” she replied.
And then it became clear who is who.
In the Alps
Three tourists have an argument regarding the way they should go. Hans says that Emanuel lies. Emanuel claims that Hans and Philip speak the same, only doesn’t know whether truth or lie.
So who is lying for sure?
Coins
Imagine there are 3 coins on the table: gold, silver, and copper. If you make a truthful statement, you will get one coin. If you make a false statement, you will get nothing.
What sentence can guarantee you getting the gold coin?
Solutions
Pandora’s Box I
The given conditions indicate that only the inscription on the lead box is true. So the ring is in the silver box.
Pandora’s Box II
The ring must be in the golden box, otherwise all the inscriptions would be either true or false.
Lion and Unicorn
As there is no day when both of the beings would be lying, at least one of them must have spoken the truth. They both speak the truth only on Sunday. However, the Lion would then be lying in his statement, so it couldn’t be said on Sunday. So exactly one of them lied.
If the Unicorn was honest, then it would have to be Sunday – but previously we proved this wrong. Thus only the Lion spoke the truth when he met Alice on Thursday and spoke with the Unicorn about Wednesday.
Island Baal
Conjunction used by A is true only if both parts are true. Under the assumption that B is an honest man, then A would be honest too (B says so) and so B would be a liar as A said, which would be a conflict. So B is a liar. And knowing that, B actually said that A is a liar, too. First statement of A is thus a lie and B is not a lying monkey. However, B is lying which means he is not a monkey. B is a lying man. The second statement of A indicates that A is a monkey – so A is a lying monkey.
Truth, Lie and Wisdom
Let’s assign a letter to each goddess. We get these sentences.
1. A says: B is Truth.
2. B says: I am Wisdom.
3. C says: B is Lie.
First sentence hints that A is not Truth. Second sentence is not said by Truth either, so C is Truth. Thus the third sentence is true. B is Lie and A is Wisdom.
In the Alps
The only one who is lying for sure is Philip. Hans speaks probably the truth and Emanuel lies. It can be also the other way, but since Hans expressed himself before Emanuel did, then Emanuel’s remark (that he does not know whether Hans is lying) is not true.
Coins
“You will give me neither copper nor silver coin.” If it is true, then I have to get the gold coin. If it is a lie, then the negation must be true, so “you give me either copper or silver coin”, which would break the given conditions that you get no coin when lying. So the first sentence must be true.