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b8+ Kxb8
e8=Q+
b8+ Kxb8
e8=Q+
b8+ Kxb8
e8=Q+
b8+ Kxb8
e8=Q+
b8+ Kxb8
e8=Q+
b7 = Q+
b8Q+ Kxb8 e8Q+ Kc7 Qe7+ Kc8 Be6+ Kb8 Qd8+ Ka7 Qc7+ Ka6 Bc8#
It’s fairly straight-forward, but a long line in order to force mate without ever giving Black a chance to promote one of his pawns (with check) or letting the King escape through b4. It’s an amusing dance of colors, because White’s bishop is limited to squares of one color, but mate in no more than 9 moves:
1. b8=Q+ Kxb8
2. e8=Q+ Kc7
2. … Ka7; 3. Qa8+ Kb6; 4. Qb7+ Ka5; 5. Qb5 mate
3. Qe7+ Kc8
3. … Kb8; 4. Qd8+ Ka7; 5. Qa8+ Kb6; 6. Qb7+ Ka5; 7. Qb5 mate
3. … Kb6; 4. Qd8+ Ka6/Ka7; 5. Qa8+ Kb6; 6. Qb7+ Ka5; 7. Qb5 mate
4. Be6+ Kb8
5. Qd8+ Kb7
5. … Ka7; 6. Qc7+ and either 6. … Ka6; 7. Bc8 mate or 6. … Ka8; 7. Bd5 mate
6. Bd5+ Ka6/a7
7. Qa8+ Kb6
8. Qb7+ Ka5
9. Qb5 mate
Not hard. White has a forced mate starting with b8 and promoting the second pawn on e8 with check. Bishop and queen force the black king round to a5 and the queen mates on b5.
But this is an odd position. It might be a composed puzzle, but given that it is check, check, check all the way to mate, there is an unusual number of irrelevant black pieces on the board. And if it is from an actual game, I can’t see how black would have obtained 2 unchallenged pawns on the 7th rank without already having had an obvious opportunity to promote one and win.
1. b8=Q+ (if 1. … Kd7 then Qd8 mate) 1. … Kxb8 2. e8=Q+ (if now 2. … Ka7 then 3. Qa8+ Kb6 4. Qb7+ Ka5 5. Qb5 mate) 2. … Kc7 3. Qe7+ (3. … Kb8 4. Qb7 mate so) 3. … Kb6 4. Qb7 Ka5 5. Qb5 mate
1.b8=Q+ Kxb8
(1…Kd7 2.e8=Q#)
2.e8=Q+ Kc7
(2…Ka7 3.Qa8+ Kb6 4.Qb7+ Ka5 5.Qb5#)
3.Qe7+ Kc8
(3…Kb6 4.Qb7+ Ka5 5.Qb5#)
(3…Kb8 4.Qd8+ Ka7 5.Qa8+ Kb6 6.Qb7+ Ka5 7.Qb5#)
4.Be6+ Kb8 5.Qd8+ Kb7
(5…Ka7 6.Qc7+ Ka8
(6…Ka6 7.Bc8#)
7.Bd5#)
6.Bd5+ Ka7 7.Qc7+ Ka6 8.Qc6+ Ka7 9.Qb7#