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Retrograde backgammon puzzle

Posted By: playBunny
Date: Saturday, 2 March 2013, at 9:52 p.m.

In Response To: Retrograde backgammon puzzle (Timothy Chow)

Q: Who is on roll? A: Blue.

The only way for White to reach the ending position is with bar/21 24/21. Coming off the bar means having been hit on the previous roll by two of Blue's men coming off the bar. If it's to be White on roll now then Blue must have had a roll after White made the anchor and that would have brought a further pair of Blue's men off the bar. However that's impossible as there are only three of Blue's men in White's home table.

I assume that any solution which puts men on the bar has to show how they got there.

Move number 1: White to play 11

White22

 ' ' '1O1O1O1X1O ' ' ' '

1O1O1O ' ' ' ' ' '1X1O '
Blue94
Position ID: FSCQCoAAAQAAAA Match ID: MIEkAAAAAAAE

White moves 15/14* 7/6*/5*/4*

Move number 2: Blue to play 42

White18

 ' ' '1X ' ' '1O ' ' ' '

1O1O1O ' ' ' ' ' ' '1X '
Blue123

Blue moves bar/23 bar/21*

Move number 3: White to play 61

White39

 '1O '1O ' ' '1O ' ' ' '

1O1O1O ' ' ' ' ' ' '1X '
Blue117

White moves bar/24* 14/8*

Move number 4: Blue to play 65

White32

 '1O '1O ' ' '1X ' ' ' '

1X1O1O ' ' ' ' ' ' ' ' '
Blue149

Blue moves bar/20 bar/19

Move number 5: White to play 11

White32

 '1O '1O1O1O '1X ' ' ' '

1X1O1O ' ' ' ' ' ' ' ' '
Blue138

White moves 8/6*/5*/4*

Move number 6: Blue to play 43

White28

 '1O '1X ' ' ' ' ' ' ' '

1X1O1O ' ' ' ' ' ' ' ' '
Blue153

Blue moves bar/22 bar/21*

Move number 7: White to play 43

White49

 '1O1O1O ' ' ' ' ' ' ' '

1X1O1O ' ' ' ' ' ' ' ' '
Blue146

White moves bar/21 24/21

Final position: Blue on roll

White42

 '1O1O1O ' ' ' ' ' ' ' '

 '1O1O2X ' ' ' ' ' ' ' '
Blue146

White Blue
1) 11: 15/14* 7/6*/5*/4* 42: bar/23 bar/21*
2) 61: bar/24* 14/8* 65: bar/20 bar/19
3) 11: 8/7/6*/5*/4* 43: bar/22 bar/21*
4) 43: bar/21 24/21

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