So, where do you live?

Logic Level 3

Abe, Buddy, Carmen, Dennis and Earl all live on Pine Street which has house numbers from 10 to 110, both inclusive. Two of them, live in the same house. The others all live in different houses. They all have made remarks about where they live, but not all remarks are true.

Abe said, "My house number is a factor of Buddy's house number.Earl house number is 10 more than Dennis's."

Buddy said, " My house number is greater than 70. Abe's house number is greater than 30."

Carmen said, "My house number is both a cube and a square. Dennis's house number is greater than 50."

Dennis said, " My house number is a square. Buddy's house number is a cube."

Earl said, "My house number is twice that of Buddy's."

But who is telling the truth? It turns out that all statements made by people living in houses with numbers greater than 50 were false. All other statements were true.

Find the sum of B+C+D+E, where:

B is the house number in which Buddy lives.
C is the house number in which Carmen lives.
D is the house number in which Dennis lives.
E is the house number in which Earl lives.

Can you catch some liars for me. Here are some of them who make statements worth deceiving

Image credit: www.phrasemix.com

The answer is 231.

2 solutions

Tran Hieu
Jun 16, 2016

Nice problem

First, we could see that everyone who said his house number greater than 50 (or any value after 50) is a liar. Because if they said the truth then there will be contradict.

Second, C's statement said that his house number is both cube and square, and within 10 to 110 only 64 satisfy that. Therefore C is a liar. That show D's house number <50 and D is a truth teller.

D said that his house number is square, then it will lies on 16,25,36,49 (we will come back to this later). His second statement said that B's house number is cube, which is true.

From B's statement (which is a liar) we can deduce 50< B's house number <70, therefore B's house number is 64 (a cube). His second statement show us that A's house number <30 and A is a truth teller.

A's first statement shows us that his house number is 16 (only factor of 64 which is >=10 and <=30). His second statement show that E=D+10.

E's statement show that he is a liar, and his house number is greater than 50. Combine that with the previous truth we can see D's house number is 49 and E's house number is 59 (the only combination that satisfy E = D+10).

So now we see that A,B,D,E live in different houses, therefore C has to living with one of those. We already know that C's house number is greater than 50, and cannot be 64, so C's house number is 59

We got our answer 64+59+49+59 = 231

Thanks a lot. And that's a very nice solution. Presented in an organized manner. (+1).

Abhay Tiwari - 4 years, 12 months ago

Saya Suka
Mar 19, 2021

10 ≤ A, B, C, D, E ≤ 110

"It turns out that all statements made by people living in houses with numbers greater than 50 were false. All other statements were true."

B : B > 70 { self-claimed liar }
==> 50 < B < 70
==> A < 30 { so A is truth teller }

A : A|B & E = D + 10

E : E = 2B { self-claimed liar, since B himself is already a liar }
==> E = D + 10 > 50
==> D > 40

C : C = n^6 { self-claimed liar since 1^6 < 10, and 3^6 > 110, while 2^6 > 50 }
==> D < 50 { so D is truth teller }

D : D = x² & B = y³
==> 40 < x² < 50, D = 49
==> E = D + 10 = 59
==> 50 < y³ < 70, B = 64
==> A|B & 10 ≤ A < 30, A = 16
==> C > 50 and C ≠ n^6, C = 59

Answer
= B + C + D + E
= 64 + 59 + 49 + 59
= 231

So, where do you live?

Can you catch some liars for me. Here are some of them who make statements worth deceiving

The answer is 231.

2 solutions

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