British Problem Solving Championship – the solutions

British Problem Solving Championship

Earlier this week we gave you the solutions of the three problems from the International Solving Contest. The annual British Problem Solving Championship saw many leading solvers gathered in Oakham, England, just a few weeks after the ISC. The BPC was a runaway success for John Nunn, who led from start to finish and solved every problem except one. The leading scores (from a possible maximum of 65) were:

Full results are available here.

In March John sent three problems for our readers to solve. Now he provides the solution, extensively explained in his trademark didactic style.

In a mate in two, it’s often a good idea to see what would happen if it were Black to move. Here the results are rather surprising, since a queen move allow Re6#, a knight move allow Rf3# and ...d5 allows Qxe5#. In other words Black is already in zugzwang, and if White had a waiting move then the problem would be solved. Of course, that would be too easy and it doesn’t take long to see that there is no waiting move, for example 1 Bf2? allows Black to take on a1 with check. The bishop on g1 is a bit of a mystery, since it played no role in the above lines and it is hard to imagine that its only function is to prevent a check along the first rank. This suggests that the key should be a white rook move to allow the bishop into play. 1 Re2? fails to 1...Ne4 and if the rook moves to, say, d3 then Black just takes on a1. By a process of elimination one arrives at 1 Rc3!, which at first sight is the least likely move because it not only unpins the queen but even allows it to check. However, it turns out that Black is again in zugzwang, although the variations are now rather different:

Most queen moves (including the checks) are met by 2 Rf3# or by taking the queen with the rook. However 1...Qxc3 2 Qxc3# and 1...Qd4 2 Bxd4# are special cases, the latter line making use of the bishop. [Click to replay]

This problem caused chaos in the British Solving Championship, with only three solvers scoring at all and only myself gaining the maximum five points by finding every variation. A certain amount of luck is involved in solving a problem like this quickly. There are many points the solver can focus his attention on, but the most productive one is to imagine what happens if Black plays 1...g3. This is an awkward move to meet because it gives the king an escape square on g4, and there aren’t very many White moves which cope with it. The key is 1 Bxe5, which threatens 2 Qg3 (threatening 3 Qxg4# and 3 Qf4#, and if 2...fxe5 then 3 Qxe5#). This move copes with 1...g3 automatically, since White can again play 2 Qxg3. There are several variations, some of them quite tricky in themselves:

To get full marks you had to give all these lines.

There are several factors which make this problem tricky. The first is that there is a quiet (that is, non-checking) threat. The second is that if you notice in the diagram that 1...Kxe4 can be met by 2 Qb4+ Kf5 3 e4#, then you will be reluctant to give this mate up. The third is that it would easy to miss White’s second move after 1...dxe2 or 1...fxe5 and thus reject 1 Bxe5. [Click to replay]

In this selfmate, White plays first and forces Black to mate White on Black’s fifth move at the latest. Black is trying to avoid mating White.

Here there are only two Black moves to worry about, 1...hxg1B and 1...hxg1N, since Black’s three other legal moves all mate White instantly. It seems likely that 1...hxg1B will be met by a series of checks ending with a check on e3, forcing Black to play ...Bxe3#. Likewise, the knight promotion will probably be met by a series of checks ending with a check on f3.

Let’s first suppose that Black plays 1...hxg1B in the diagram (we don’t know yet what White’s first move is). It seems unlikely that the final check will be delivered with the black king on c5, since it would have to be by Qxe3+, and at the moment there is no need for Black to take on e3 as the king can move to c4 or d6. So probably the king will be chased somewhere making it easier to force the capture on e3. Then it’s a case of looking at forcing sequences of checks to see what comes up. After a bit of trial and error, it should be possible to find the sequence 1...hxg1B 2 Rxc6+ Kxc6 3 c8R+ Kb7 4 a6+ Ka7 5 Qxe3+ Bxe3#. The main trouble here is that this line already works in the diagram, so it gives little clue as to White’s first move, other than that it should not disrupt this pre-existing line.

Here’s where it helps to guess the idea of the composers. This line features a rook sacrifice, followed immediately by the rebirth of the rook via a pawn promotion. Could something similar happen in the other line? The only other piece which can be sacrificed immediately is the white queen, and if White played Qd6+ followed by f8Q+ then we would have a sequence analogous to the first one. Since this also provides a role for the f7-pawn, which has hitherto played no part in the proceedings, we are probably on the right lines. The obvious problem is that Qd6+ can at the moment by met by ...Kxc4, which suggests that White’s first move must eliminate this possibility. The bishop must stay on c4 to cover a6 in the first line, so 1 b3 is a likely key (indeed, otherwise it’s hard to see what the b2-pawn is there for). Then we have the two lines:

Astronomy

Never a Nunn without an astronomical reference. Chess, problem solving and chess publication is John's "day job". At night (somewhere in the world) he spends his time working with a global network of remotely operated telescope systems. Global Rent-a-Scope (GRAS) allows subscribers to connect to worldwide telescope locations and operate the instruments there. In an article on the GRAS site John explained how image processing can be used to enhance the pictures one takes with the remote telescopes.

Above is a John Nunn image (which you can click to enlarge) of two galaxies in the constellation Leo, M65 (on the left) and M66 (on the right). This pair represents two-thirds of the famous ‘Leo triplet’, but unfortunately the remaining one (NGC 3628) is too far away to lie in the field of view of the telescope he used, G11.

In his GRAS article John tells GRAS visitors how to use deconvolution, a mathematical technique for removing blurring, in order to enhance the images that come out of the telescope, how to combine sub-frames to make a colour image, and how to use other techniques to achieve the perfection you see in the example above. Very instructive.

Links to previous problem articles