A palindrome is a number that reads the same backward as forward (for example 101). What is the next greatest palindrome after 3443?

Hint: To solve this question first, we will understand the definition of the palindrome. After this, we will fix 3 at a thousand places in 3443 and try to determine the next number in palindrome form such that it is near to 3443.

Complete step-by-step solution:
It is already given in the question that a palindrome is a number that reads backward as forward. Here, we are given our number as of 3443. Now, as we want the next palindrome after 3443. So, to do this we will fix 3 at the thousand’s place. Now, as 3 is fixed at the thousand’s place and the number obtained should be a palindrome then the last digit the one’s place should also be 3. So, we have obtained
3 _ _ 3
Now, we need the greater number 3443. The next digit greater than 4 is 5. So, 3553 can be possible.
Also, if we are assuming 5 at tens place, then 5 should be present at a hundred’s place also as we need the number to be a palindrome. Hence, the next greatest palindrome after 3443 is 3553.

Note: Here, 5335, 4334, 4114, 3553, etc. all are also possible. But what we need is the next palindrome after 3443. Basically, we need the nearest palindrome after 3443. This can only be obtained by fixing 3 at a thousand’s place and then proceeding for the number greater than 4.