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# Traveler problem : Choosing right street between varying answers

## Question

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.

## Recommended Posts

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Spoiler

Take number 27 (the middle road)

The first 4 villagers can not be "useless" based on the possible outcomes of their clues. This leaves the remaining villagers. Only 1 combination of numbers leaves 3 of them giving useless information (15, 27, and 39 would have villagers 7, 8, and 9 giving useless information. From there its just a matter of testing the remaining outcomes.

 15 27 39 1 W R W 2 R W W 3 W R W 4 W W R 5 R W R 6 R W R 7 U U U 8 U U U 9 U U U 10 W R W 11 W R W

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