Brain Teasers
The Number Lier
There are 3 numbers 0-9.
Eric knows the product and says, "I know the numbers."
Then, everyone is told that one digit is exactly one greater than another.
Then, Luke is told one of the numbers and says, "Eric lied."
Then you are told the numbers add up to 11.
What are the numbers?
Eric knows the product and says, "I know the numbers."
Then, everyone is told that one digit is exactly one greater than another.
Then, Luke is told one of the numbers and says, "Eric lied."
Then you are told the numbers add up to 11.
What are the numbers?
Answer
0, 5, 6Eric knows the product and claimed that he knows the numbers.
Luke is told a number and then he knows Eric lied.
If Luke had received an 8, the combination could be 8,8,8, which is the only combination that multiplies to 512; Luke wouldn't know Eric lied.
If Luke received 6, the combination could be 6,7,7 which is the only combination that multiplies to 294, so Luke wouldn't know Eric lied.
If Luke received 2 or 7; 2x7x7=98.
4 or 5; 4x5x5=100.
3 or 9; 3x9x9=243.
1; 1x1x1=1.
Luke would only know that Eric lied if Luke was given a 0.
Therefore one of the digits is 0.
The remaining two digits must add to 11 because 11-0=11.
Two of the digits are one apart so that leaves:
0 & 1 + 10
5 & 6 + 0
However, 10 isn't an option so it must be 0, 5, 6.
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Comments
It took a billion submissions, but I got it.
My Goodness! At the time I read this teaser the difficulty was 1.6. Was it fairly obvious to everyone else that you had to run through all possible numbers Luke knew to eliminate everything but zero? I found this very difficult. Very interesting puzzle, but I could not find the logical path to the solution.
Once it was established that people could lie, I could not rule out the possibility that Luke also lied. But, that was not a big distraction. I assumed Luke told the truth.
Once it was established that people could lie, I could not rule out the possibility that Luke also lied. But, that was not a big distraction. I assumed Luke told the truth.
Sorry for my slump of teasers, snowdog
No apologies! I love your teasers. I went through your entire collection after the first Cake teaser because I wanted more. I did it again after this one, just to make sure I had not missed any of your puzzles. If you are building these from scratch, I'm really impressed and look forward to more! Just wonderful, even if they flummox me.
I get some inspiration, for example, I saw "how to find patient zero", and that inspired the cake disaster, that was the biggest inspiration
I agree with Snowdog - I don't follow your logic. Also, I think you meant "Liar". Not sure what a "lier" is...???
I agree with Snowdog - I don't follow your logic. Also, I think you meant "Liar". Not sure what a "lier" is...???
I do follow the logic presented in the answer. I just could not find it on my own. I like this puzzle more every time I think about it.
I think you may be misunderstanding it a bit, wolf
Luke knows the number & it's the only one that Eric wouldn't know the combination to
Luke knows the number & it's the only one that Eric wouldn't know the combination to
The scip model that I used to solved this can be found at https://gist.github.com
/33fcc44936807b0583c2f63cfc90c6fa
/33fcc44936807b0583c2f63cfc90c6fa
I found it very hard, but got it once I looked at the answer...
Umm, how do we know Luke isn't lying?
Because it's called the number liar, not the liar liar
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