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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

567.0. "The Keyboard Game" by MODEL::YARBROUGH () Wed Aug 20 1986 20:04

Here's an interesting little game you can play with a pocket calculator.
It was originally published in an early issue of the now-defunct magazine 
"Creative Computing".

Two players compete in the Pocket Calculator Keyboard Game. They play on 
the square numeric keypad of the calculator, which is assumed to look like:

		7 8 9
		4 5 6
		1 2 3

One player selects and announces a key to be the first used. The other
player selects and announces a starting value, >100, to be entered into the
calculator. The first player then subtracts the value of the starting key
from the starting value. Thereafter the players alternate, selecting a key
ADJACENT TO THE LAST KEY as the next value to be subtracted. (If the last 
key used was '1' then 4, 5, and 2 are legal choices for the next move.) The
player who last produces a value >= 0 wins. 

Who wins, and what is the winning strategy?

(There are several variant games; for example, include the zero key, 
representing 10 in the subtraction. There are variations on this because
the zero key is located differently on different calculators, e.g. adjacent
to the 1&2, or to the 1,2,3; even next to the 6&9 keys.) 

Lynn Yarbrough
T.RTitleUserPersonal
Name		DateLines
567.1brute forceLATOUR::JMUNZERFri Aug 22 1986 20:434
    Looks to me like the first player can just go to his corner (any
    corner), but that he needs an end game handbook.
    
    John
567.2CLT::GILBERTeager like a childFri Aug 22 1986 22:3969
Here is a list of 'won' positions.  The number at the left is what's showing
on the calculator, and the columns represent the previous players number.

We see that the corners should be avoided, and we formulate the following
strategy.  If the displayed number is > 12, then choose a corner number,
and take the smallest corner value that does not leave your opponent a
value of 56, 39..41, 22..26, or 10.  If the displayed value is <= 12, ...
work it out yourself.

    1 2 3 4 5 6 7 8 9
  0 . . . . . . . . .
  1 . W . W W . . . .
  2 W W W W W W . . .
  3 . W . . W W . . .
  4 W W . W W W W W .
  5 W W W W . W W W W
  6 . W W . W W . W W
  7 W W W W W W W W W
  8 . . . W W W W W W
  9 . W . W W W W W W
 10 W W W W W W W W W
 11 . W . W W W W W W
 12 . W . W W W . W .
 13 . W . W W W . W .
 14 . W . W W W . . .
 15 . W . W W W . . .
 16 . W . W W W . . .
 17 . W . W W W . . .
 18 . W . W W W . . .
 19 . W . W W W . W .
 20 . W . W W W . W .
 21 . W . W W W . W .
 22 . W . W W W W W W
 23 . W . W W W W W W
 24 . W . W W W W W W
 25 . W . W W W W W W
 26 . W . W W W W W W
 27 . W . W W W . W .
 28 . W . W W W . W .
 29 . W . W W W . W .
 30 . W . W W W . W .
 31 . W . W W W . . .
 32 . W . W W W . . .
 33 . W . W W W . . .
 34 . W . W W W . W .
 35 . W . W W W . W .
 36 . W . W W W . W .
 37 . W . W W W . W .
 38 . W . W W W . W .
 39 . W . W W W W W W
 40 . W . W W W W W W
 41 . W . W W W W W W
 42 . W . W W W . W .
 43 . W . W W W . W .
 44 . W . W W W . W .
 45 . W . W W W . W .
 46 . W . W W W . W .
 47 . W . W W W . W .
 48 . W . W W W . . .
 49 . W . W W W . W .
 50 . W . W W W . W .
 51 . W . W W W . W .
 52 . W . W W W . W .
 53 . W . W W W . W .
 54 . W . W W W . W .
 55 . W . W W W . W .
 56 . W . W W W W W W
 57 . W . W W W . W .
...(the pattern for 57 now repeats indefinitely).
567.3more messy end gamesLATOUR::JMUNZERTue Aug 26 1986 21:0111
"To grandmasters, it may turn out that the dismaying message of the latest
computer analysis is that concepts do not always work in the endgame.
Sometimes the direction of play seems deliberate and purposeful.  At other
times, the computer wins by playing in ways that seem to have no logic."

From a NY Times (8/26/86) article reporting that a computer program has
disproved the commonly accepted win/draw statuses of several end games,
such as KQ vs. KBB and KQP vs. KQ.  The program works backward from mates
to winning/drawing positions.

John