OzProblems update on display of twin positions

Regular visitors to OzProblems will be familiar with the idea of twinning, which is a common way of expanding a problem’s content. In twin problems, the diagram position is solved normally, but additional solving positions are formed by adjusting the diagram as described – such as shifting a piece to another starting square. The task remains the same, but each simple change leads to a significantly different solution. Traditionally these added positions are given in text only; however, with our site update they are now viewable as diagrams without requiring extra space.

As illustrated by the problem below, twin positions are indicated by the dots below a diagram. Click on the diagram and use the arrows that appear to view the twins. On a touchscreen, you can also swipe the diagram. The number of dots represents how many parts there are, and the highlighted dot (moving left to right) corresponds to the position currently displayed. This method of showing multiple images in one spot is called a “carousel” in my website-builder, and the widget is also used on the AI images page of my other site. I’m not sure why it took me so long to realise such a feature is great for presenting twin problems!

This two-mover employs progressive twinning – indicated by the “&” – which is slightly different from the standard type. In standard twins every specified change is made to the diagram position, whereas in progressive twins each additional position modifies the previous part. So while part (b) is derived from the diagram (a) as usual, (c) is produced by making a further change to (b), and (d) is produced by adjusting (c). Hence, the removal of a black piece here in each twin leads to a continuous drop in the total number of units.

The four parts of this problem are solved by different moves of the g6-bishop, all of which threaten 2.Rg8 (the flight-move 1…Kd8 doesn’t stop the threat). In (a), White begins with 1.Bh5! to preserve the B + R battery. The set reply to the black knight’s strong defence is thereby retained: 1…Sd7 2.Rf8. In (b) without the knight, 1.Bh5? fails to 1…Rc1! The key 1.Bc2! precludes the rook pin and there is no defence against the threat. In (c), a random bishop move is defeated by black castling. Therefore 1.Bd3! to prepare for 1…0-0-0 2.Bxa6. In (d), Black has yet another strong defence that refutes most bishop moves, 1…Ra1! So 1.Bb1! to prevent the pin, and because the a6-bishop is gone, 1…0-0-0 now permits 2.Rc1. The changed mates against black castling are a nice touch in this problem that shows thematic twinning. The persistent removal of pieces to create twins is called the striptease theme.