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What is the sum of all three-digit odd integer palindromes?

 Jul 30, 2021
 #1
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The sum is 40500.

 Jul 30, 2021
 #2
avatar+34380 
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Can you explain how you derived that answer?  

ElectricPavlov  Jul 30, 2021
 #3
avatar+114511 
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Mmm they must end in 1,3,5,7, or 9

1a1        10     sum = 10(101)+450 

3a3         10    sum = 10(303)+450

5a5         10    sum=  10(505)+450

7a7         10

9a9          10

 

for each a can be any integer from 0 to 9

 

So I get 50 numbers

The sum of 0+10+20+ ..... 90 = 5(0+90) = 450

10(101)+450

 

Total sum = 10(101+303+505+707+909) +5*450 = 10*2525 + 1250 = 26500

 

That is what I get but I haven't checked it for careless errors

 Jul 31, 2021

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