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What is the sum of all the 5 digit palindromes?

 Jun 13, 2021
 #1
avatar+114102 
+2

What have you looked at so far

 

abcba

any digit can go in the middle,  How many is that?

a can't be 0

So there are 9 choices for a and 10 choices for b.

 

So how many altogether?

 Jun 13, 2021
 #3
avatar+287 
+1

Wait!  The question is not asking for how many 5-digit palindromes there are.  It wants the sum of all those palindromes instead.   For example, were I to change the 5 to a 2, the situation would be like this.   There are nine 2-digit palindromes: 11, 22, 33, 44, 55, 66, 77, 88, and 99, but the sum of all the 2-digit palindromes is $11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99 = 495$.
 

Bginner  Jun 13, 2021
 #2
avatar+23 
0

Well, that would be 8100*c and c is also 10 so it would be 81000

 Jun 13, 2021
 #4
avatar+114102 
+1

Let's see

 

abcba

any digit can go in the middle,  How many is that?  10

a can't be 0

So there are 9 choices for a and 10 choices for b.

 

So how many altogether?

 

10*9*10=900  exist.

 

Oh dear, Bginner is right, they are asking for the sum of them

 

ok

sum of 100c is  100(0+1+2+...9)=100(45)=4500

sum of 10001+20002+ ..... +90009 = 10000(1+2+...9) + (1+2+...9) = 10000*45+45 = 10001*45=450045

sum of 0000+1010+2020 .... 9090 = 45(1000+10) = 45*1010 = 45450

4500+450045+45450 = 499995     that is what I get but I havn't checked it.  I could easily have miscounted.

 Jun 14, 2021
edited by Melody  Jun 14, 2021
edited by Melody  Jun 14, 2021

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