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THIS WAS problem 2 in the Christmas Quiz. Black to play 64. Should he play: (a) 8/2, 6/2 (b) 13/3* (c) 10/6, 10/4?

What is black's plan? Before the roll he trails in the race by 31 pips, so he cannot hope to win unless he can stall white by hitting a shot at some point. He needs to stop the white man on his 3-point either escaping to the outfield with a 6 or linking with the men on his bar-point with a 4.

Note also that white owns the doubling cube, so black must win with his men - he has no recourse to the cube.

Given this general plan, black has two options - he can hit immediately or he can prepare to hit next time. After either option white has some horror numbers, such as 41 if black hits, 53 if he doesn't. Should black fear a return hit by white? To some extent, yes - but with white's 5- and 6-points open he should have no trouble re-entering. So which of these three moves best achieves black's objectives?

As with many backgammon problems, aggression wins the day. The immediate hit with 13/3* is correct - and correct by a large margin. Both Snowie and Jellyfish confirm this. As well as putting the plan into action immediately rather than preparing to do so, it has the bonus of winning quite a lot of gammons when white fails to re-enter for a few rolls.

When this position occurred at the Double Fives I was the captain of the team playing black. I insisted on hitting, white rolled 35 from the bar (one of the horror rolls with the other plays) hitting my blot; I then stayed on the bar for 9 rolls while white brought all his men home and won a gammon. Such is the perversity of the game!

THANKS TO the many of you who took the time to enter this year's difficult quiz.

Congratulations to the winners. First prize goes to Michael Howard of Newbury. Receiving runners-up prizes are Andrea de Zandonati of Venice, Donald Godden of Bristol, Cedric Lytton of Sheringham, and Derek Irwin of Fulham in west London.