A palindrome problem!

Probability Level 3

What is the number of palindromes which have $2x$ digits,where $x>0$ . If the answer is of the form, ${A \times B^{x-C}}$ ,where $A,B,C$ are positive integers and $A$ is as small as it can be,then what is the value of $A+B+C$ ?

The answer is 20.

1 solution

Adarsh Kumar
Jul 20, 2015

From the above image we have that the total number of palindromes of $2x$ digits $=9\times 10^{x-1}$ ,hence $A=9,B=10,C=1\Longrightarrow A+B+C=20$ .And done!

Moderator note:

Are those values of $A, B, C$ uniquely determined? Why can't there be other such triplets?

Nice diagram ! Upvoted :).

Venkata Karthik Bandaru - 5 years, 10 months ago

Thanx a lot!

Adarsh Kumar - 5 years, 10 months ago

I am really sorry sir,I have made the required corrections.

Adarsh Kumar - 5 years, 10 months ago

If $F(x)=A\times B^{x-C}=9\times 10^{x-1}$ , then $\frac{F(1)}{F(0)}=B=10$ And $F(0)=A\times 10^{-C}=9\times 10^{-1}$ $A=9\times 10^{C-1}$ The smallest integer value for $A$ is $A=9, C=1$

Joan Palacios Beltran - 5 years, 10 months ago

A palindrome problem!

The answer is 20.

1 solution

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