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Counting PUZZLE

Posted By: Nack Ballard
Date: Friday, 3 May 2024, at 10:36 p.m.

In Response To: Counting PUZZLE (Bob Koca)

Yes. One can map a one-to-one correlation on the moves that play a 4 or 5 from the 8pt in Paul's position versus the moves that play a 4 a 5 from the 7pt in my variant, except: in my variant, 13/8 8/4 is distinct from 13/8 7/3.

I'll leave this as an exercise for the reader: If you change the roll from 54 to 64...

(a) Why is the number of legal moves diminished (from 17 or 16) to only 13? (See diagram pair below.)
(b) Why is the number of legal moves the same (13) in both positions with a roll of 64, whereas there is a difference of 1 when the roll is 54?

[Bob: In your poser, it seems to me that Student A has double-counted all the fifth-student inclusions by allowing both perspectives. I run across these tile-draw-counting probability situations in Scrabble pre-endgames and thankfully make fewer mistakes now.]

Nack





White is Player 2

score: 0
pip: 112
Unlimited Game
Jacoby Beaver
pip: 105
score: 0

Blue is Player 1
XGID=--ACCbB-B---bBB----cbbbb--:1:1:1:64:0:0:3:0:10
13 legal moves
White is Player 2

score: 0
pip: 112
Unlimited Game
Jacoby Beaver
pip: 103
score: 0

Blue is Player 1
XGID=--ACCbBB----bBB----cbbbb--:1:1:1:64:0:0:3:0:10
13 legal moves

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