Q: What is the largest four digit palindrome?

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A palindrome reads the same forward and in reverse. This tells me that at leastthe first digit and the last digit must be the same. So it's not possible to have a6-digit palindrome "with no same digits".The largest 6-digit palindrome, with just enough repetition of digits to make it apalindrome and no more, would be 987,789 .

8778

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the answer is ofcourse 9999. If you insist that the first and second digit be different then it would be 9889.

8778

If you allow non integers, then your smallest four-digit number would be .0001. If you only allow integers, then your smallest four-digit number would be 1000. Your largest four-digit number would be 9999.