\[ \large \dbinom{n}{r} \quad , \quad \dbinom{n}{r+1} \quad , \quad \dbinom{n}{r+2} \quad \]

###### Image Credit: Wikimedia TED-43.

For some integers \(n>r>0\), the values of the three binomial coefficients above are all palindromes with more than one digit. Find the minimum possible value of \(n+r\).

Note: These numbers are written in decimal representations.

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