Can you win this puzzle?

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ArdyLee
Hi, I just tried this puzzle, I was just wondering, could you actually check mate in this position? Because the puzzle stops there, and black will check mate us in the next move.
ArdyLee

bigD521

If I am seeing this correctly it is whites turn to move and should play 1. Bg4. This protects the h3 pawn and prevents black from creating a draw by 3 repetitive positions. If Blacks plays Qf3+ the king must move to e1. Qf2+ then the king must move back to d1. As long as black keeps checking on those squares it ends in a draw.

Also Black cannot mate - If 1. ... Qf2+ or Qg2+ 2. Qe1 stops it. If 1. ...... Qd2+ 2. Qxd2

Currently white is up a rook and two pawns, so yes this should lead to mate with best play. Move 7. Bg4 shows almost a 6 point advantage.