You are looking through the most advanced telescope.. You see that there is Martians in Mars! Not only that but they are sitting on a classroom doing math! This is what their board says:
3*3=9 // 4*4=15 // 10*10=100
How many fingers (or tentacles) do they have?
Molok
Favorite Answer
the highest digit visible is 9 so the number system base is at least 10.
10*10=100 is true in all bases so there's no information there
3*3=9 is consistent in any base greater than or equal to 10
4*4=15 cannot be in base 10 so the base of their number system is larger than 10
the entire number 15 is in the form 1*base^1 + 5^base^0
you know that in decimal 4*4=16 the lowest digit of an integer in any base is always "the one's column" or "base^0 = 1"
so you're safe computing 16-5 = the value of the next column since the digit in that base^1 column is 1.
16-5 = 11
so the number is in base 11 and if you presume that all civilizations count on their fingers and that they use standard indo-arabic numerals, it would mean that martians have 11 fingers.
you can check this by plugging the martian digits into the equation:
1*11^1 + 5*11^0 =
1*11 + 5*1 =
11 + 5 =
16 which is the correct decimal value for 4*4