K+P vs K+P Puzzle by Zavodny

White to move and force mate in as few moves as possible. 

a8=Q!

Kb1 Qe4+ (Kc1? Qc2#) (Ka1? Qxa3+ Kb1 Qb2#) Ka2 Kc2! Ka1 Qe1+(or Qh1+) Ka2 Qb1# 

a2 Qh1# nicee~ ..

 nevermind my comment. Your notation confused me a bit.

I think the shortest one is 

1. a8Q Kb1 

2 Qa4 Ka2

3. Kc2  Ka1

4. Qa3# 

Qe4-a3??????????????????????????????

murometzyx> 1. a8=Q Kb1 2. Qe4+ Ka2 3. Kc2 Ka1 4. Qe1+ Ka2 5. Qb1#

That's a mate-in-five, but there's a faster solution.

neneko> 1. a8=Q Kb1 2. Qa4 Ka2 3. Kc2 Ka1 4. Qxa3#

Very good, but a mate-in-three is possible. Can anyone spot it?  :) 

does it begin with kb3 ?

neneko> I can't find one in 3. Everything I see that's possible ends with black getting a stale mate.

 It's tricky, but it's there, and it sounds like you're on the right track.

WEdgards> does it begin with kb3?

Nope. 

1. Kb3 would have black move the king away 1. ...Kb1 and black escapes the trap so you won't get mate in the next few moves.

1. Kc2 would have black move 1. ...a2 wich would force you to retreat your king or it will be a stalemate. Black escapes the trap on this one too.

1. a8Q is the only meaningful move left. Black move 1. ...Kb1

Next move you can't move closer with the king so the queen is the only possible piece to attack with.

 2. Qe4 leads to murometzyxs sollution and Qa4 leads to mine.

2 Qa3 is a stalemate.

Am I missing something? 

Situations where rook underpromotions lead to a faster win crop up from time to time in pawn endgames. For example:

ok. it was just a try to solve the problem .. to gave mate # .. the next step is to mate black faster .. :)

yes.. nice one!!

a8=R!! realy faster!

 murometzyx> a8=R!! realy faster!

Glad you figured it out the rest of the moves.  :)

there are a few mates in 3 but they are not forced. The black king can go from A2 to B1 and back to prolong the game.

nice one!