Scorpions In My House?

Logic Level 2

Anna, Eva and Tatiana visited my house one day. The following conversation took place:

Anna : Wow, this house has more than 100 scorpions!
Eva : No, I saw at most 100 scorpions in this house.
Tatiana : I know that I saw at least one scorpion.

If only one of these girls told the truth, how many scorpions are in my house?

There are no scorpions! Between 1 to 99 scorpions Exactly 100 scorpions There are more 101 or more scorpions

1 solution

Fayssal Abdelli
May 20, 2016

Relevant wiki: Truth-Tellers and Liars

Anna's proposition : > 100 scorpions
Eva : <= 100 scorpions
Tatiana : >= 1 scorpions

The propositions of Anna and Eva are contradictory. So, they can't tell truth or lie in the same time. One of them is saying truth and the other one is lying.
Because only one of those three girls is saying truth, it means that Tatiana is telling a wrong proposition.
We have then to take the contradictory of Tatiana's proposition.

<1 scoprions are in my house !
So, 0 scorpions are in my house :)

The problem is unclear because the house having a certain number of scorpions and the number of scorpions seen are 2 different things.

For example, let the house house have 1000 scorpions in. Eva had a good look around and saw 200 of them, and Tatiana only had a brief look and didn't see any. Then, Anna is telling the truth and the other 2 are lying.

Alex Chatfield - 5 years ago

Hi. But the question is : How many scorpions are in my house. If there are 1000 and Eva saw only 200, her response will be incorrect because it doesn't match the exact number of scorpions in this house :) Of course, we consider that all the scorpions have been seen in this house :)

Fayssal Abdelli - 5 years ago

Where does it say "that all the scorpions have been seen in this house"?

That is a highly unrealistic assumption.

I'm saying that the question as it is, is incomplete.

Alex Chatfield - 5 years ago

The converse of Tatiana's statement would be 'There is at most 1 scorpion', which means there are scorpions <= 1. Therefore you cannot nail down 0 as the only answer. Consider editing your problem or answer. :)

Nilabha Saha - 5 years ago

Hi Saha, thank you for your remark :) However, the reverse of the statement X >= 1 is not X<=1 but X<1 ;) So the logical reverse of this proposition "I know that I saw at least one scorpion" is the following : "I know that I saw less than one scorpion".

Fayssal Abdelli - 5 years ago

sorry, but who exactly again among the three girls is the only one who tells the truth? i don't yet get why 0 is the answer.

Geneveve Tudence - 5 years ago

Hi. The last one is not saying truth because the first girl and the second contradict themselves. So; one of them is saying truth and the other one in laying. They can't say truth and lie in the same time because they contradict themselves ... Because we have only one girl who saying truth and it's the first or the second. The third girl is automatically laying :) The third said : >= 1. You take the reverse of this proposition ... So you take < 1 . 0 is the solution :)

Fayssal Abdelli - 5 years ago

you just said that one of the 1st 2 girls is saying the truth, so one of these 2 assumptions MUST be true : 1- there are more than 100 scorpions Or 2- there are at most 100 scorpions if the 1st statement is true , then the answer cannot be = 0 if the 2nd statement is true , then there is at least 1 scorpion and EVA said " i saw.." and we are taking her statement to be the truth in this 2nd condition or statement

-and i want to stress that "EVA" said " i saw..." so eva's answer cannot be interpreted as she did not see any scorpions-

Ziad Osman - 5 years ago

@Ziad Osman – Hi Zied, If the first assumption is true, it means that the third girl is saying truth because 100 is greater than 1. Or, in our case, we need to solve this exercice assuming that only one girl is saying truth. For the second step now : When I say : I saw less than 100 scorpions. This assumption is equivalen to say : I didn't see anything OR I see between 1 to 99 scorpions :) Perhapse the term used (SAW) is confusing ... But take it easy !

Fayssal Abdelli - 5 years ago

Statement 2 and 3 indicate how many scorpions they SAW. Just because something was SEEN or NOT SEEN does not mean it does or does not EXIST. Given that, let's work through each person's statement assuming it is true:

If one statement is true, we must check the other two to make sure they are false.

Anna - TRUE - Exist > 100 scorpions Is it possible Anna did not see <100 scorpions? Yes, since more than 100 exist. Is it possible Tatiana did not see any scorpions? Yes, she could be blind, or not looking. Therefore, Anna can be telling the truth.

Eva - TRUE - Saw <= 100 scorpions Is it possible the house does not have more than 100 scorpions in it? Yes, Eva at most saw 100. Is it possible Tatiana did not see any scorpions? Yes, she could be blind, or not looking. Therefore, Eva could be telling the truth.

Tatiana - TRUE - Saw >= 1 scorpion Is it possible Anna did not see <100 scorpions? Yes, since we only have a minimum of 1. Could see 101 Is it possible the house does not have more than 100 scorpions in it? No. for Anna to be lying, she had to see 101 or more. If she saw 101 or more, the house DOES have more than 100, so Anna would be telling the truth. This scenario doesn't work.

Result: Anna or Eva could be the only one telling the truth. We do not know which is the truth teller. If Anna is the truth teller, the house has more than 100 scorpions. If Anna is a liar, the house has 100 or less scorpions.

We cannot know the answer given these parameters.

Greg Wallace - 5 years ago

Hi Greg. Nice analyse but the final result is not good after all. you said that : [Anna or Eva could be the only one telling the truth. We do not know which is the truth teller] ... Yes, it's correct. Only one of them is saying truth but not both ... Because we have only one who saying truth, the third person is laying automaticlly because we know that one of the two first girls is saying truth ! The reverse of the third statement is <1 ... The third person is laying, so you take 0 to justify that this person is laying.

Fayssal Abdelli - 5 years ago

Scorpions In My House?

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