# Traveler problem : Choosing right street between varying answers

A Traveler is going to a town, but he must pass a strange village,
From the village there are 3 streets, only 1 street leads him to the town,
He doesn't know which street he must choose,
The villagers are giving the streets name with numbers written in local symbols,
The traveler can not read the symbols.

1st villager : "Take the street with a cube number."
2nd villager : "Take the street with lowest number."
3rd villager : "Take the street with middle number."
4th villager : "Take the street with higest number."
5th villager : "If you divide the right street number (RSN) with 8, the remaining is 7."
6th villager : "If you divide RSN with 24, the remaining is 15."
7th villager : "If you divide RSN with 12, the remaining is 3."
8th villager : "If you divide RSN with 4, the remaining is 3."
9th villager : "If you divide RSN with 6, the remaining is 3."
10th villager : "If you divide RSN with 5, the remaining is 2."
11th villager : "If you divide RSN with 7, the remaining is 6."

After finding so varying answer, he decided to ask the chief of the village,

The chief than giving him this right information :

"we are numbering streets with numbers between 10 to 50,
The left street has lowest number,
The right street has higest number,
The front street has bigger number than left street,
3 villagers give you useless answers,
4 villagers give you right answers,
and 4 villagers give you wrong answers"


What are the street numbers ? Which street he must choose ?

Note :

Useless answer means if you know the numbers, the answer is right to all numbers, so it is useless.
right answer means the answer is leading you only 1 street, and it is the right street.

• downvotes ? I think community here do not like math puzzle. – Jamal Senjaya Aug 31 '16 at 8:41
• How is that 9 different answers? I see 11... – Tim Couwelier Aug 31 '16 at 8:59
• @JamalSenjaya you can never guess what others like .......if some people like it implies that some others will not like it.. – Amruth A Aug 31 '16 at 9:08
• @AmruthA Thank you. I just wonder why some person easily downvote a puzzle, I got 4 downvotes at first. – Jamal Senjaya Aug 31 '16 at 9:25

because:

First it's clear that none of the statements 1 to 4 can be useless. Therefore all useless statements are the remainder statements from 5 to 11. The below table lists all the possible road numbers (10 to 50) in the rows, and each statement from 5 to 11 in the columns. Each entry is 1 if true, 0 if false. It can be seen that only 4 rows contain 3 or more ones, therefore the useless statements must apply to 3 of these 4 rows. In fact the only way to choose 3 rows and columns such that all 9 entries are 1, is to choose columns 7,8,9 and rows 15,27,39. This implies that 7,8,9 are useless statements and the road numbers are 15,27,39. If we assume that 27 is the correct road then everything works:

1. correct
2. wrong
3. correct
4. wrong
5. wrong
6. wrong
7. useless
8. useless
9. useless
10. correct
11. correct

Total correct = 4, total wrong = 4, total useless = 3.

• So he must choose the front street. – Jamal Senjaya Aug 31 '16 at 10:22

The correct street number is possibly:

39

• Why do you think your answer is right? – Jamal Senjaya Aug 31 '16 at 9:55
• Because according to statements of the villagers and the chief of the village the number ranges between 10 to 50 and , four villagers are right , four are incorrect, 39 number satisfies all above so...I will add the explanation. – user28797 Aug 31 '16 at 10:11
• good guess, but still wrong. To know your answer is right or wrong, you have to reveal all the numbers. – Jamal Senjaya Aug 31 '16 at 10:17