# 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 gave 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 the lowest number."
• 3rd villager: "Take the street with middle number."
• 4th villager: "Take the street with the highest number."
• 5th villager: "If you divide the right street number (RSN) with 8, the remainder is 7."
• 6th villager: "If you divide RSN with 24, the remainder is 15."
• 7th villager: "If you divide RSN with 12, the remainder is 3."
• 8th villager: "If you divide RSN with 4, the remainder is 3."
• 9th villager: "If you divide RSN with 6, the remainder is 3."
• 10th villager: "If you divide RSN with 5, the remainder is 2."
• 11th villager: "If you divide RSN with 7, the remainder is 6."

After finding so varying answers, he decided to ask the chief of the village. The chief than giving him this correct information:

We are numbering streets with numbers between 10 to 50. The left street has the lowest number. The right street has the highest number. The front street has a bigger number than the left street. 3 villagers gave you useless answers, 4 villagers gave you correct answers, and 4 villagers gave 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 for all numbers, so it is useless.
• Correct answer means the answer leads you only 1 street, and it is the right street.
• downvotes ? I think community here do not like math puzzle. Commented Aug 31, 2016 at 8:41
• How is that 9 different answers? I see 11... Commented Aug 31, 2016 at 8:59
• @JamalSenjaya you can never guess what others like .......if some people like it implies that some others will not like it.. Commented Aug 31, 2016 at 9:08
• @AmruthA Thank you. I just wonder why some person easily downvote a puzzle, I got 4 downvotes at first. Commented Aug 31, 2016 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. Commented Aug 31, 2016 at 10:22

The correct street number is possibly:

39

• Why do you think your answer is right? Commented Aug 31, 2016 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
Commented Aug 31, 2016 at 10:11
• good guess, but still wrong. To know your answer is right or wrong, you have to reveal all the numbers. Commented Aug 31, 2016 at 10:17