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what is the sum of all three-digit odd integer palindromes that contain a digit of 2?

Aug 2, 2021

#1
-5

#Palindromes are basically numbers that read the same forward and backwards, like 16861

The information three digit odd palindromes give us valuable information. From this we know that both the hundreds digit and the ones digit must be 1,3,5,7 or 9.

Since we need to contain a digit 2, that could now only fall under the tens digit because both the hundreds and the ones digit must be odd.

So, the possible palindromes are:

121

123

125

127

129

321

323

325

327

329

521

523

525

527

529

721

723

725

727

729

921

923

925

927

and 929.

Adding all of them together we get: (121*5+2+4+6+8) + (121*5 + 200*5 +2 +4 +6 +8) + (121*5 + 400*5 +2 +4 +6 +8) + (121*5 + 600*5 +2 +4 +6 +8) +(121*5 + 800*5 +2 +4 +6 +8)

which equals (121*5 +2+4+6+8)*5 + 1000 +2000 + 3000 + 4000

which sums up to 13125, which is the final answer.

Aug 2, 2021
#3
+1

Ooops !   Red numbers are not palindromes: 121

123

125

127

129

321

323

325

327

329

521

523

525

527

529

721

723

725

727

729

921

923

925

927

and 929.

Guest Aug 2, 2021
#2
+2

Three digit ODD palindromes that have a '2' in them :

121

323

525

727