Checkmate Puzzle

Question

I had a chess position today, in which my last position had 5 possible moves to checkmate. This seemed like a lot to me, and I immediately thought of the puzzle: Which position would yield the maximum number of ways to checkmate the opponent on the next move?

The rules of my made up puzzle are thus

1. Exactly 1 King per side
2. Any amount of any other kinds of pieces are allowed for either side
3. "Score" for the position is the number of winning moves there are

I came up with the following position. By my count, this has 70 total winning moves. I wonder what the maximum would be?

Follow up puzzles which occurred to me:

1. What's the fewest number of pieces for which every legal move would be checkmate?
   • Pawns aren't allowed
   • Exactly 1 King per side
   • White to move. All black pieces are counted in the answer
   • Alternate rule: you can only have one kind of piece, so there's a unique answer for each kind of piece
2. What's the fewest number of points for which every legal move would be checkmate?
   • Pawns aren't allowed
   • Exactly 1 King per side
   • White to move. All black pieces' points are counted in the answer
   • Q=9,R=5,B=3,N=3,K=3

Anyone have any suggested solutions to the above puzzles?

Answer 1

Unless I'm misunderstanding the rules, you can easily construct cheap forced mates by

putting white in check: (4 non-Kings, 16 14 points)

And along the same lines, some single-piece boards:

three queens or rooks, five bishops, or five knights should do the trick:

Answer 2

So many questions in one. Here's my answer to the follow-up question(s):

3 pieces, 13 points:

Which can be achieved like this:

White's only legal move is Kxb3#.