We are going to play a regular “find my number” game, i.e. you announce your initial guess and following my answer ( limited to: “more “, “less” or “right!”) go on to your next guess.
Usually to reveal a number from 1 to N you need no more than log₂N guesses in the worst case.

How many guesses are needed if I told you that my number is a 4-digit palindrome divisible by 7 ?

Assume the worst case, of course.