Four white markers are placed on the first four squares of a row of nine squares. There is a space of one square and then four black markers.
• White markers can only move right.
• Black markers can only move left.
• Markers can move forward one square, or can jump over a marker of either colour if there is an empty square to land on.
• Markers are not removed from the board if jumped.
• You DO NOT have to alternate moving black and white markers.
How can you get the markers to exchange places?
+---+---+---+---+---+---+---+---+---+
| W | W | W | W | | B | B | B | B |
+---+---+---+---+---+---+---+---+---+
clc
global history
board=['r1';'r2';'r3';'r4';' ';'l1';'l2';'l3';'l4'];
history={board};
addon
function addon
global history
board=history{end};
bareBoard=board(:,1);
blank=strfind(bareBoard',' ');
if isequal(bareBoard,['llll rrrr']')
disp(' ')
disp(length(history))
for i=1:length(history)
disp(history{i}')
disp(' ')
end
else
for i = 1:length(board)
if bareBoard(i)=='r'
if i==blank-1 || i==blank-2
saveBoard=board;
saveHist=history;
board(blank,:)=board(i,:);
board(i,:)=' ';
history{end+1}=board;
addon;
history=saveHist;
board=saveBoard;
end
elseif bareBoard(i)=='l'
if i==blank+1 || i==blank+2
saveBoard=board;
saveHist=history;
board(blank,:)=board(i,:);
board(i,:)=' ';
history{end+1}=board;
addon;
history=saveHist;
board=saveBoard;
end
end
end
end
end
finds two symmetric ways of accomplishing the task, one starting on the left and one on the right. The number of moves in each is 24, so we show 25 states, starting with the original state and ending with the final state. The markers are labelled with their direction of travel, with the rightward ones initially on the left labelled 'r' and the leftward ones initially on the right labelled 'l'. Each set of four is numbered 1-4 from left to right.
White pieces move right and are labeled 'r'.
Black pieces move left and are labeled 'l'.
25 25 states (0 through 24)
rrrr llll initial state
1234 1234
rrr rllll r4 moves forward
123 41234
rrrlr lll l1 jumps him
12314 234
rrrlrl ll l2 moves forward
123142 34
rrrl lrll r4 jumps him
1231 2434
rr lrlrll r3 jumps l1
12 132434
r rlrlrll r2 moves forward
1 2132434
rlr rlrll l1 jumps him
112 32434
rlrlr rll l2 jumps r3
11223 434
rlrlrlr l l3 jumps r4
1122334 4
rlrlrlrl l4 moves forward
11223344
rlrlrl lr r4 jumps him
112233 44
rlrl lrlr r3 jumps l3
1122 3344
rl lrlrlr r2 jumps l2
11 223344
lrlrlrlr r1 jumps l1
11223344
l rlrlrlr l1 moves forward
1 1223344
llr rlrlr l2 jumps r1
121 23344
llrlr rlr l3 jumps r2
12132 344
llrlrlr r l4 jumps r3
1213243 4
llrlrl rr r3 moves forward
121324 34
llrl lrrr r2 jumps l4
1213 4234
ll lrlrrr r1 jumps l3
12 314234
lll rlrrr l3 moves forward
123 14234
llllr rrr l4 jumps r1
12341 234
llll rrrr r1 moves forward
1234 1234
and starting move in the other direction:
25
rrrr llll
1234 1234
rrrrl lll
12341 234
rrr lrlll
123 14234
rr rlrlll
12 314234
rrlr rlll
1213 4234
rrlrlr ll
121324 34
rrlrlrl l
1213243 4
rrlrl lrl
12132 344
rrl lrlrl
121 23344
r lrlrlrl
1 1223344
rlrlrlrl
11223344
lr rlrlrl
11 223344
lrlr rlrl
1122 3344
lrlrlr rl
112233 44
lrlrlrlr
11223344
lrlrlrl r
1122334 4
lrlrl lrr
11223 434
lrl lrlrr
112 32434
l lrlrlrr
1 2132434
ll rlrlrr
12 132434
lllr rlrr
1231 2434
lllrlr rr
123142 34
lllrl rrr
12314 234
lll lrrrr
123 41234
llll rrrr
1234 1234
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Posted by Charlie
on 2022-11-16 09:36:29 |
computer solution (spoiler)
