First!..... Well in my house. :)  This one looked like it would be easy but I struggled.  Got it though.

1. Bd1 is necessary for the mate in four because it covers the g4 and h5 squares.

Easy. All forced moves!

Second Night Sleepless In Reykjavik, l'ISLANDE. 1.Bd1 Bg6 2.Rg4+ Kh5 3.R4xg6+ Kh4 4.Rxh7+#  Hello! More Nice Is 4.Rh6+# OK  Confused In Brainfog. Easeland Want, For The Sake Of Beauty, To Sacriface A Rook For One Bishop Mitre On Square g6: 2.R3xg6 hxg6 3.Rxg6... Intending 4.g3+ Kh3 5.Bg4+# I Am Lost In A Fog. Thank You Anyway, chess.com  Auf Wiedersehen

bad puzzle

Of course it is better to take a pawn and give checkmate, instead of just giving checkmate.  It is like a bonus pawn.  If the value of the move is considered mathematically then you are looking at (∞ + 1) or just ∞, and those are mathematically equal; but it is not necessary to look at these as a one-dimensional sum.  In a two-dimensional plane a rectangle that is zero height and ∞ length has area zero, but if has height 1 pawn and length ∞ (checkmate pawn equivalent points) then the area is ∞, so that is much better. In this calculation the unit of area is square pawns, denoted P^2 or pawns^2, or in Algebraic Notation, just ^2.

Nice one!

what is this i dont even

too easy :{)

E-A-S-Y   P-E-A-S-E-Y

got it by trying every move on the board.

Lg6?? Rab8! and no mate

Good puzzle. 

2 Solutions

@Cavatine, what are you talking about? So what if the rectangle has a square pawn level of near infinity? In a tournament its worth one point and that's it. Really man, this is not the place to show off mediocre math jargon.

wow. I've loved it

This one was a pretty tricky one for me

Why did you say a lot of people were confused?

Very nice.  I've had sticky bishops in real games.  The discovered check was elegant.  Thanks chess.com.  That one was worthy.