Griff's Riddle #1

[griffman]

Four natives on an island were asked to explain their system of numbers.

Native 1 said: "18 is a prime number and so is 41."
Native 2 said: "7 x 8 = 62."
Native 3 said: "35 is a prime number."
Native 4 said: "63 is evenly divisible by 4."

Two of the natives were telling the truth; two of the natives were lying. What is the base of their number system?


I will give hints as this goes on. It's not an easy one (especially if you don't Google it...)

[Night Ω Wolfe]

And googling it is against the rules so don't take Grif's comment as a suggestion

[griffman]

OK so the first hint, since it has been a couple days...

Native 4 is one of the two natives lying.

[AREA666]

I think fixing the typo for native 2 was a better hint. I was all confused about it a few days ago and was going to ask what you meant by it, but now it makes more sense so I can return to being confused by the riddle, and maybe I can eventually make an educated guess.

[griffman]

Yeah I don't know why exactly I had such a bad typo. I usually catch that as I type... that was the night I stayed up way late, but I posted it hours before I went to sleep so that wouldn't be a good excuse...

[aule]

base 9

natives 1 & 2 are telling the truth, converted to base 10 they say

1: 17 is a prime number and so is 37
2: 7 x 8 = 56
3: 32 is a prime number
4: 57 is evenly divisible by 4


reason, native 2 used 7 and 8 thus it had to be at least base 9 otherwise they would not know 8

then i assumed 2 was right, being the easiest to test on another base and it worked out alright for base 9, then i checked the other 3 and i found 2 correct and 2 false


Edit: I had base conversions last semester though mostly base 10 to base 2 but we did see some general rules

[griffman]

Congratulations Aule! Very good logic there looks like you get to make the next riddle. Good luck

[Night Ω Wolfe]

Jeez even with an explanation I am still confused haha... great job!