Question

Numerical palindromes A palindrome is an integer, such as 45654, that reads the same backward and forward. (a) How many five-digit palindromes are there? (b) How many n-digit palindromes are there?

Answer 1

Please, Anyone ?

Answer 2

for 5-digit polindromes, we can form it like ABCBA
for the first digit A, we can choice 9 ways
for the second digit = 10 ways
for the third digit = 10 ways
and the rest is only 1 way
so, totaly is 9 x 10 x 10 = 900

Answer 3

corect me if im wrong, @rational :D

Answer 4

in order ro solve (b) we have ... (n-2) * (n-1) * n * 1 * n * (n-1) *(n-2)....

Im not even sure if that makes sense..

Answer 5

IN fact i would say:

\[n*(n-1)*(n-2)................1...................(n-1)*(n-2)*n\]

Answer 6

or maybe \[\sum_{i=1}^{m}(n-m+k)\] where k =1 and n at some point has to be equal to m

Answer 7

yes looks good to me :) \[ABCBA\]

total number of 5 digit palindromes = \(9*10*10\)

because the last two digits are determined by first two digits.

Answer 8

Similarly if \(n=2k+1\) is odd, then the total number of \(n\) digit palindromes is
\[9*10^{k}\]

Answer 9

and if \(n=2k\) is even, then the total number of \(n\) digit palindromes is
\[9*10^{k-1}\]

Answer 10

k has to be an integer as well i gues..

Answer 11

i dont get it, if k =1 for an even number, what does it mean ?

\[9*10^{1-1}= 9*1\]

Answer 12

or if k equals zero for an even number:

\[ 9 * 10^{-1}\]

Answer 13

n = 2k

is an even number no matter what the value of k is

Answer 14

n = 2k+1

is an odd number no matter what the value of k is

Answer 15

they are the definitions of even and odd numbers

Answer 16

look for example when k is less or equal to 0 we have number like this

\[9*10^{-2}\] = \[9*{\frac{1}{10^{2}}} \]

Answer 17

i guess speaking of palindrums this number does not represent at all this concept

Answer 18

Notice here "n" represents number of digits, so what do you mean by a number having negative number of digits ?

Answer 19

and that's why i said k has to be equal or greater than 2

Answer 20

;d anyway thanks for helping me out