Grandmaster Gary and Loudmouth Larry

White to Play and Mate in 10,
with the Knight,
without capturing any Black pawns

5K1k/8/3R4/2B3p1/6Pp/4pP1P/4P2P/7N w
(Problem composed by Horowitz)

Grandmaster Gary and Loudmouth Larry were playing their usual weekly game. Gary was about to play Rh6 mate when Larry snarls, "Let me guess... you're gonna mate me with your Rook, right?"

"Is there any reason why I shouldn't?" Gary calmly replies.

"Yea, if you think you're so good, why don't you mate me with a different piece!"

"And which piece would you like me to mate you with?" Gary asks.

Larry studies the board for a moment and replies, "Why don't you mate me with your Knight..."

"Okay," Gary replies.

"...without capturing any of my pawns!!" Larry finishes.

Gary looks again at the position and nods his head. "Okay. Not only will I mate you with my knight, and not capture any of your pawns, I'll do it in ten moves.

Can Gary make good his statement?

White to Play and Mate in 8,
with the pawn,
without moving his King,
and Black promises to promote to a Queen.

k7/1RKR4/1P1p4/8/8/8/8/8 w

How Grandmaster Gary and Loudmouth Larry reached this position would probably make for another story, but let's ignore that for the moment and listen in...

"Here we go again... Rd8 mate right?" Larry quips.

"Well, would you rather I mate you a different way?" Gary asks.

Larry thinks he has Gary this time. He ponders for a moment and says, "If you're all you say you are, then I challenge you to mate me with your pawn! Furthermore, you can't move your King to do it!"

Gary studies the position for a moment and replies. "I can do so... in eight moves, providing that you promote your pawn to a Queen."

Larry hesitantly agrees.

The task looks impossible. How can Gary do it?

White to Play and Mate in 3,
with the rook on the "a" file,
without moving it.

"I think I gotcha Larry," Gary quips. "It's mate in three. I think you're powerless to stop my Rook to a1, then Bd2 and then Rh1#."

Larry looks at the position and agrees. "Well, I bet you can't mate me with that rook in three moves without moving it."

Gary studies the position and boasts that it can be done.

How?

White to Play and force
Black to Mate in 5.

2B5/p2Q4/1P6/2P5/3P2n1/4P1Pk/5Pp1/6K1 w - - 0 0
(Problem composed by Rubin)

"Larry sees that Gary is about to play Qxg4# and quickly says, "Hey Gary! How about if we try something different this time. How about this time the winner buys dinner?"

"The winner? That seems rather odd," Gary replies.

"What's the matter? Afraid you'll beat me?"

Gary studies the position and says, "Okay, I agree. It just so happens I'm in the mood for lobster tonight. I hope you can afford it!"

How should Gary, as White, proceed in order to force Black to win in just five moves?