White to play and win Can't capture black rook as there is a stalemate.

good theme.  a lot of variants with the same end position to get there.

Good theme, but there ae many solutions, as the rooks can block the checks too!

if rook blocks, wont it end in stalemate?

the rooks can't block the checks anywhere, because most of the time the rook is adjacent to the white king, and if it isn't, the intermittent squares can't be reached by white's rooks.

 The key point about the solution is that now Black is unable to continue checking the white king without allowing one of White's rooks to act (demolishing the last hopes for a draw), nor can he neglect checking the white king as the outcome would be the same. It's lose-lose for black!

Why can't you move to g7 on the sixth move (6.Kg7)?

Yes rooks cannot block check There can be many routes to end position One way is given as solution Key is to find the final location

 

good theme - there is a similarity with :

 1. "very cramped position" puzzle [on this site] - my solution [a National Master's solution was different and more generally applicable, but no similarity with this]

 2. mate with K+B+N  v K

3. bridge endplays and squeezes, in that:

 you visualise where to get to achieve your goal, and then play to get there.

 

thats a nice one.....probably why one should play till the end....you win only when you checkmate....convert winning positions to a win