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The answer is 58.

56+57+58 = 171

171 is the largest palindrome less than 220 that can be divided by three.

Further palindromes are: 181, 191, 202 and 212.

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Q: If a sum of a particular set of 3 consecutive positive integers is a 3mdigit palindrome and the sum is less than 220 what is the greatest possible value for the largest of the 3 integers in the set?
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