Alien's Calculation

For students of class 6-8 (age 12 to 14)
siwomcre
Posts:7
Joined:Wed Dec 21, 2016 5:00 pm
Alien's Calculation

Unread post by siwomcre » Fri Jan 06, 2017 10:32 pm

Aliens have been found in Mars who have six fingers in each of their hands, total
12 fingers in their two hands. We use 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 to do all the
calculation, and they use 0, 1, 2, 3, 4, a, 5, 6, 7, 8, 9, b. So, 10, 11, 12 in earth is 9,
b, 10 in Mars. Find the square of 1b in aliens’ system.

What is the solution ?

Absur Khan Siam
Posts:65
Joined:Tue Dec 08, 2015 4:25 pm
Location:Bashaboo , Dhaka

Re: Alien's Calculation

Unread post by Absur Khan Siam » Sat Jan 07, 2017 5:07 pm

Solution :
The problem statement assures that the aliens use $12$ based number system.So we can covert this in the way how we convert decimal to binary or octal or hexa and so on.First we can make a chart:
Decimal -> Aliens($12$ based)
  • $ 0 -> 0$
    $ 1 -> 1$
    $ 2 -> 2$
    $ 3 -> 3$
    $ 4 -> 4$
    $ 5 -> a$
    $ 6 -> 5$
    $ 7 -> 6$
    $ 8 -> 7$
    $ 9 -> 8$
    $ 10 -> 9$
    $ 11 -> b$
So $1b = 1*(12^1) + 11*(12^0) = 12 + 11 = 23$
So $(1b)^2 = 23^2 = 529$
Now convert it into 12 based system as you convert decimal to binary.Instead of dividing by $2$ divide by $12$.
Convert the remainders according to the chart.For example:If you get a remainder $5$ replace it by $a$ .
If you do this correctly you will get the answer $371$.
"(To Ptolemy I) There is no 'royal road' to geometry." - Euclid

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