Unknown Number Logic

Logic Level 3

Arton and Billy are each given a positive integer, and they are told that the two positive integers are consecutive. The following conversation ensues:

Arton: "I don't know your number."

Billy: "I don't know your number either."

Arton: "Now I know your number!"

What is the largest possible value for Billy's number?

This is one part of 1+1 is not = to 3 .

The answer is 4.

5 solutions

Kenneth Tan
Jul 30, 2014

Arton's number can't be 1 because if he is 1 then he would have immediately guessed out Billy's number which is 2 but instead he said he doesn't know. If Arton's number is 2, he will think whether Billy's number is 1 or 3, since Billy said that he doesn't know either, then Billy's number can only be 3. If Arton's number is 3, Billy's number cannot be 2 because if he is 2 he would have guessed out Arton's number which is the same situation as if Arton's number is 2, so Billy's number is 4.

i dont understand something...How arton can surely say,"Now i know" ?Colan could write any two consequetive positive numbers.And then they would still be unsure about others number

Nakibur Rahman - 6 years, 2 months ago

Excellant job,

Chandrachur Banerjee - 6 years, 10 months ago

How would 3,4 work because if first no. Is 3 other no. Could be both 2 and 4 but if other no. Is 2 then its done but if equals 4 how can he be sure

Chaitnya Shrivastava - 5 years, 4 months ago

Soumava Pal
Aug 11, 2014

yes the immediate response is 4 but there can be many such solutions right?

There are only 2 solutions in this problem, but if you limit the numbers in a range, for example, if Colan wrote two consecutive numbers ranging from 1 to 100, then there would be 4 solutions: $(2,3),~(3,4),~(97,98),~(98,99)$

Kenneth Tan - 6 years, 9 months ago

Rajeshree Deotalu
Jul 29, 2015

I did it in same way. !!!! Surely there will be several answers but I start with 1,2,3....so I got it correct. !!!

Fuad Muhammad
May 25, 2015

I think the answer can be 4, 6, or 8

Auzi Asfarian
Aug 1, 2014

The answer is 4, but it is only my lucky guess to answer the minimum number that meet the criteria of the question. Many others possible answer exist, for example:

Arton has 8, Billy has 9. Arton has 14, Billy has 15.

In this two possible answers, Arton can definitely guess Billy's number is he know that Billy's number is not a prime.

In first example, Billy's possible answer are 7 and 9. 7 is prime, so 9 is the answer.

In second example, Billy's possible answer are 13 and 15. 13 is prime, so 15 is the answer.

Or perhaps there is another clue that I miss :(.

The thing is, that Arton doesn't know about the the prime number clue. There are two solutions and you are supposed to write the one, which is not prime

Simona Vesela - 6 years, 10 months ago

Unknown Number Logic

This is one part of 1+1 is not = to 3 .

The answer is 4.

5 solutions

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