# Bases?!?!

• Oct 30th 2006, 11:43 AM
t-lee
Bases?!?!
Find the missing numbers in the following sequence:
10,11,12,13,14,15,16,17,20,22,24,31,100,____,____

I don't know where to start. I know that we have been working with different bases in my math class but I can't think of where to start. Can you explain to me how this works?
• Oct 30th 2006, 11:58 AM
topsquark
Quote:

Originally Posted by t-lee
Find the missing numbers in the following sequence:
10,11,12,13,14,15,16,17,20,22,24,31,100,____,____

I don't know where to start. I know that we have been working with different bases in my math class but I can't think of where to start. Can you explain to me how this works?

What does this have to do with bases?

-Dan
• Oct 30th 2006, 02:42 PM
Soroban
Hello, t-lee!

This is a classic (old) problem . . .

Quote:

Find the missing numbers in the following sequence:
10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, 31, 100, __, __

The next two numbers are: 121 and 10000.

The number "sixteen" is written in base 16, 15, 14, 13, 12, ... , 4, 3, 2.

Check it out . . .

$\begin{array}{cccccccc}16 = 10_{16}\\ 16 = 11_{15} \\ 16 = 12_{13} \\ \vdots \\ 16 = 31_5 \\ 16 = 100_4 \\ 16 = 121_3 \\ 16 = 10000_2\end{array}$

• Oct 30th 2006, 04:38 PM
ThePerfectHacker
Quote:

Originally Posted by Soroban

This is a classic (old) problem . . . [/size]

How many "classic riddles" do you know. It seems anyone asks a question you have an answer in the response of a "classic riddle". It is horrific.
• Oct 30th 2006, 04:45 PM
topsquark
Quote:

Originally Posted by Soroban
Hello, t-lee!

This is a classic (old) problem . . .

The next two numbers are: 121 and 10000.

The number "sixteen" is written in base 16, 15, 14, 13, 12, ... , 4, 3, 2.

Check it out . . .

$\begin{array}{cccccccc}16 = 10_{16}\\ 16 = 11_{15} \\ 16 = 12_{13} \\ \vdots \\ 16 = 31_5 \\ 16 = 100_4 \\ 16 = 121_3 \\ 16 = 10000_2\end{array}$

Hah! I love it!! :cool:

-Dan