Communicating with Brill the Ant

Number Theory Level 2

As Brill the Ant has 6 legs, she operates in a base 6 system. We want her to know that 100 students are working on this problem. What is the units digit when 100 is written in base 6?

Details and assumptions

You may choose to read about Number Base Representation .

The answer is 4.

4 solutions

Đinh Việt Thắng
Sep 15, 2013

100=2 6^2+4 6+4 Thus 100(10-base)=244(6-base)

Moderator note:

The most common mistake made was to not realize that the question asked for the unit's digit , which is 4, as opposed to the entire value, which is 244.

i did the same but just wrote 244 , and they crossed it

Ahsan Latif - 7 years, 8 months ago

Me too, for the first time. We should read more carefully

Đinh Việt Thắng - 7 years, 8 months ago

same :v

Seno Dibyo - 7 years, 8 months ago

couldnt understand

Kinjal saxena - 7 years, 8 months ago

Let N be a number. Unit place of representation of N in base B contains digits between 0 and B-1. Divide N by B. The remainder is unit place digit of N in base B.

Kunal Das - 7 years, 8 months ago

In this case, 100/6 has remainder 4. So 4 is the unit place value at representation of 100 in base 6. The full representation of 100 in base 6 is 244

Kunal Das - 7 years, 8 months ago

There is a far simpler method to this that the other solutions - the units digit is always going to be the remainder you get when you divide the number by the base, because that's the only term that is not multiplied by 6. Thus since the remainder of 100/6 is 4, we can directly say that the units digit is going to be 4

Arjun Pitchanathan - 7 years, 8 months ago

me too

Ritwik Upadhyay - 7 years, 8 months ago