# Math Mystery

1. Oct 10, 2007

### Stevedye56

1. The problem statement, all variables and given/known data
In the binary number system 1100011 is the name for the largest 2 digit palindrome in base ten. What base 10 number does this binary number represent?

2. Relevant equations
None

3. The attempt at a solution

My question about this problem is the 2 digit part is ambiguous. Is the two digit imlplying only 2 different numbers OR is it implying two digits long? I know that 1100011=c=100 in roman numerals but 100 is not a palindrome.

I would also like to point out that this was a question given to a 6th grade math class. My friend and I are taking calculus and were confused by the problem. Any insight?

2. Oct 10, 2007

### Integral

Staff Emeritus
1100011 is odd, how could be equal to 100?

3. Oct 10, 2007

### Stevedye56

1100011 in binary code represents the letter c, therefore in roman numerals c=100. But how could there be a palindrome in base 10? It would have to end in 0 wouldn't it?

4. Oct 10, 2007

### Stevedye56

Ok we found it from last year. Apparently the answer to the question is 99, although when divided by 10 the result isnt a whole number.

5. Oct 10, 2007

### Integral

Staff Emeritus
As a binary (base 2) number 1100011 = 1*26+1*25 +0*24 +0*23+0*22+1*21+1*20 = 64+32+2+1 = 99.

You should be looking at the binary number system, not ascii characters.

This statement makes me doubt your understanding of the question. What do you think "base 10" means?

Last edited: Oct 11, 2007