Mathematical Diversions by James Alston Hope Hunter

By James Alston Hope Hunter

Mathematical diversions

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In the Queen's Gam­ bit, Black's dark-squared bishop is far too valuable a defensive piece to be exchanged in the opening with loss of time. t'xd2 6 lbc3 d5 7 e3 lbbd7 c6 8 U3 9 0-0 Allowing Black to free himself by an ingenious manoeuvre. White could have frustrated this plan by 9 l:td l ! and Black's position would have remained very cramped. 9 ... xc4 e5! lbxe5 ! , and Black equalises with ease. b3! By this move, which prevents B lack from gaining time later on with . . lbb6, White indirectly meets 1 1 ...

I'xd5). e4! 30 Now Black's queenside pawns become very threatening. The ques­ tion is, how to maintain them ! The game now enters upon its most criti­ cal phase. 3 1 lbe5 If 3 1 lbxaS obviously 3 1 . i'xd5 and Black wins easily. 31 'if5! 32 'ie2! (D) White has defended himself ex­ cellently, and hopes to obtain a deci­ sive advantage by the text move, which threatens the knight and the c­ pawn at the same time; but Black's reply gives him a disagreeable sur­ prise. •• B ••• Why not 28. lLlf3+ and 29 .

The game now enters upon its most criti­ cal phase. 3 1 lbe5 If 3 1 lbxaS obviously 3 1 . i'xd5 and Black wins easily. 31 'if5! 32 'ie2! (D) White has defended himself ex­ cellently, and hopes to obtain a deci­ sive advantage by the text move, which threatens the knight and the c­ pawn at the same time; but Black's reply gives him a disagreeable sur­ prise. •• B ••• Why not 28. lLlf3+ and 29 . . lLld2 ? 32 b3! Before deciding on this surpris­ ing move, Black had to visualise the following variations, apart from the ••• 42 Triberg 1921 continuation played in the game it­ self: 1 ) 33 11£4 'iVh5 34 1hg4 (or 34 'iVxg4 leading to line 2) 34 .

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