Number the initial checkers #25,...,#1. The leftmost checker #25 must jump over all 24 others, so its final place number is $\ge49$. If $49$ were its final position, #1 wouldn't move, so #2 would just jump over it at some point. But as long as #1 and #2 are adjacent, no checker can jump over both of them. So at least one of them must move one place to the right during the process. So $N\ge50$ and it is easy to see that the moving is possible with $N=50$. E.g., start with moving #1 one place to the right. Then in order #3, 5,...,25,24,22,...,2 jump/move to their end position, which is place number $25+i$ for checker #i.