win in 4 moves

found this puzzle in w. lewis - chess problems. i will post the solution some time later.

 

Here is what I came up with.  To me, this seems the most logical approach. White needs to rely on the black queen to check so you are able to mate in 4...

Ne5+ = Kh1

Rf7 = Qb2+

Kd1 = d3

Qg7#

However this is assuming that black has a one track mind to get a mate in 3 moves. If black plays Qf8 instead of checking, then queens may be exchanged, but mate in 4 moves is thwarted.  I do not see how Qb5 will prevent mate in 4, it seems like a wasted move because the rook is already in position to protect Qg7 for the mate.

 

the queen can keep checking the king, if say white plays something like 1.h4

black plays 1...Qb2+

2. Kd1 (only move)

2...Qb1+ 3. Ke2 (only move)

then comes 3...Qb5 (the black pawn can also check) and where ever white moves the queen can check(even though some moves would be would be a queen sacrifice) to prevent a mate in 4. the hint is that every move should be a check and finally checkmate. 

white to mate in 4, solution

 

hmm, I didn't think of sacrificing the queen.  I usually don't unless I can trade queens.  But I see what you mean by every move needs to be check.  Thanks for this puzzle.

tactician got the answers