Two weeks ago we published five Easter puzzles, the last of which did not contain a chess position but rather asked our readers to guess which World Champion lost bets on all of the other four problems – i.e. was not able to solve them in a specific period of time, or in fact at all. Here now are the solutions with comments by the author, Hungarian/US GM, penings theoretician, author and problemist Pál Benkö.
Puzzle No. 1
Mate in three moves
Solution: 1.Bc4 Ke5 2.Qd5+ Kf6 3.Qg5# – or 1...Kf5 2.Qh5+ Ke4 (2...Kf6 3.Qg5#) 3.Qd5#.
The author of the problem, Pal Benko, tells us that he gave this mate problem to Bobby Fischer at the Lugano Olimpiad in 1968, where he spent a couple days. Bobby could not solve it in half an hour and lost the bet he had made with Pal. In fact he lost a second bet, because he said that the problem must have a second solution. "I told him that was impossible," says Pal, "since I composed it when I was already fifteen years old. The next day he paid up again. I joked that it had been so hard for him because he never played the Italian Opening [with Bc4] but rather Spanish [with Bb5]."
Puzzle No. 2
Helpmate in two – A: Diagram, B: Bc1–> Bf1
Solution: 1.Nxd6 Kd3 2. Ke5 Bb2. Twin: 1.Qxd6+ Nd5+ 2.Ke6 3.Bh3#
"Bobby liked helpmates," Pal says, "so he asked me to show them to him many times. For problem two I gave him half an hour, but he was not able to do it. I don't remember the exact dates for this and the remaining helpmates."
Puzzle No. 3
Helpmate in three – two solutions
"In this puzzle I had prepared a special trick for Bobby, and he walked straight into it. I had given him the position in the evening and the next day he brought me the wrong answers."
Bobby's solution: 1.Qxe2+ Nxe2 2.Bg4 Nbc3+ (or Sec3+ or Sg3+) 3.Kf3 4.0-0# and 1.Bxe2 Nxe2 2.Qc4 Nbc3+ 3.Kd3 4.0-0-0#. However there is a problem that makes these solutions invalid. With Black to play in the diagram position what was White's last move. Obviously it coule only have been with the king, so castling must be invalid! The correct solution is:
1.Bxe2 Nxh3 2.Kf3 Rg1 3.Qe4 Rg3# and 1.Qxe2+ Nxe2 2.Kd3 Nxa3 3.Be4 Rd1#.
Puzzle No. 4
Helpmate in three
After one hour Bobby lost the bet. "Also Botvinnik, Keres and Geller could not solve it at Wijk aan Zee 1969, before we were thrown out of the restaurant :-)", writes Pal Benko (yes, the octogenarian uses smileys!). "Botvinnik was quite a good solver, but he did not like helpmates. Only Reshevsky was able to solve it in about half hour."
Solution: 1...Kb2 Rd5 2.Kc3 Rc5+ 3.Kd4 Nb3#.
Állan Ramon, Santos Nascimento, Aracaju, Brasil
I'm not a very good player, and as a med student don't have much free time. I took three days to solve the first problem, and wasn't able to solve any of the helpmates. But puzzle number five: that was Bobby Fischer, no further explanations.
Jorge, Shinozaki, Tokyo, Japan
In puzzle one it was tough to find the first move, 1.Bc4! But the rest was a piece of cake. The World Champion who lost bets on all of the problems was Bobby Fischer.
Gabor Szamosközi, Budapest, Hungary
Each puzzle was incredible wonderful! I guess the "victim" must have been Bobby Fischer.
Peter Alain Spiriev, Budapest, Hungary
I know all three solutions as Benko showed them to me in 1989 when we travalled to Baden Baden. The World Champion who missed the solution was Bobby Fischer. The solution to the first problem is 1.Bc4! but why did Fischer miss it? Because he preferred the Ruy Lopez better known as the Spanish Game with 3.Bb5, so according to Benko to start with 1.Bc4 (Italian) was a bit strange to Bobby. Of course it is not correct to participate in the competition, as I know the answers from Benko. But it was nice to remember that trip.
Mussie Mengesha, Addis Ababa, Ethiopia
Number one and two are relatively easy, numbers three and four are mind blowing. How long did it take for Mr. Benko to construct them? I simple use the trial and error method to arrive at the answers. Personally I would say these help mates are good ones for a player to develop visualization for mating patterns. And also I like the master move tactical challenge series, and wait for them eagerly. Good job ChessBase.
Ilyas Ramdzan, Skudai, Malaysia
At first I tried using the queen to prevent the king from moving away from White's side of the board with moves like 1.Qh5 and 1.Qd6, but it turns out fruitless. After a while I realized that 1. Bc4 traps the king between two diagonals where the queen can swoop in like a pin ball. After solving it I tried running it on my computer and found out that 2.Qf3 also works. Glad I didn't give up too early. Puzzle two: Beautiful!! It took a very long time to find out where the king should be mated, and it turns out you don't even need the queen! Puzzle No 4 stumped me. At first, I was trying to work out how to use the knight to block a2, and it turns out, there is a very annoying extra move for Black that won't make it happen. This suggests that the king has to move. It took an hour and a bathroom break to finally realize that I didn't need to mate the king at the edge, so I began looking at various K+R+N setups that could lead to mate. It took another hour to figure out that instead of bringing the knight to the king, the solution is the exact opposite. I don't have a clue which World Champion lost the bets, but I'm guessing it must have been someone who was close to Pal Benko. Perhaps the answer is GM Robert James Fischer.
Yamil Duba, Encarnación, Paraguay
It's amazing how the minds of GMs work. They can solve this tricky problems in 20 minutes, but it took me 50 minutes for each of them!!! Thanks for the chance of winning! Greeting from the heart of South America!
Daniel Frazón, Salto, Argentina
I know I've got just a few chances to win, as I've really did pretty badly, but I think that participation is more important. Take care and I hope I wll have good luck!
Hanon Russell, Milford, Connecticut, USA
Puzzle #1 was composed in 1968 and presented to Fischer at Lugano, 1968, with a bet he couldn't solve it in 30 minutes. He couldn't. The story is told by Larry Evans in his foreword to Karsten Mueller's book "Bobby Fischer: The Career and Complete Games of the American World Chess Champion."
Max Cheng, Los Angeles, USA
Puzzle 5: I guess Gary Kasparov, something to do with puzzle 3.
Baron Tal, Tel Aviv, Israel
Problem 5: Mikhail Tal...?
Jan Gantar, Vodice, Slovenia
I think it could be Bobby Fisher, though not because he would be a bad solver, but due to being American, like Benko.
Roberto Stelling, São Paulo, Brazil
Puzzle No. 1 is not as difficult as it may look, it doesn't take long to the solver to figure out that the white bishops need to coordinate with the queen and the best way is to keep them two columns/files appart. Puzzle No. 2 I had seen and solved in the past. It takes a certain ingeniosity to figure out that the white queen needs to be captured and once you've seen that idea in one solution the second solution becomes obvious. What always struck me though was the question: is the white queen really necessary? It seems to me that it can be taken away without affecting the solutions or causing any cooks on both twins. On the other hand all the dramatic effect vanishes when the white queen is taken away. This is the proverbial case of the baby being thrown away with the bath water! Puzzle No. 4: This is another classic Benko. After trying to give mate on the cornered black king for a while and always missing by one move or tempo the solver is eventually drawn to the idea ov giving mate on the center instead! Thanks a lot, happy Easter and congratulations to the Great Puzzle Master and player. I must mention that I met Benko once when I was just a teenager and watching helpmates for the first time in my life in 1979! I was appointed to help the great Brazilian composer Felix Sonnenfeld when he was working at the Rio de Janeiro Interzonal in 1979. Felix and Pal Benko were sometimes found in the analisys room talking about chess problems and showing each other their work. The first helpmate I ever solved was shown to me by Felix Sonnenfeld right after he'd shown it to Pal Benko!
Joshua Green, Laurel, MD, USA
Thanks for the pleasant diversion. In puzzle number one it looks like White should force the bK down the board to meet its opposite, so a natural try is 1.Qh5?. This doesn't seem to work after 1... Kd4 (the only move) as the bK flees. Mates with the wQ guarded on a square diagonally adjacent to the bK with a wB guarding Black's two flights seem to be springing up everywhere, but how to force one? Eventually one tries the correct key, and then the analysis isn't so hard as White's second moves are both checks. The Queen's moves make a very nice geometric impression. 1. Bc4! Kf5 (1... Ke5 2.Qd5+ Kf6 3.Qg5#) 2.Qh5+ Ke4 (2...Kf6 3.Qg5#) 3.Qd5#.
Puzzle No. 2: This problem strongly reminded me of an exercise in John Nunn's "Solving in Style".
Z. Zilahi, Magyar Sakkelet, 1956
Helpmate in two
This is a problem in which logic is no help – either you see the idea or you don't. 1...Qxd6+ 2.Kb5 Kd5 3.Nc3#. It is astonishing that Black has to take White's queen with check in order to arrange a mate, but this is the only solution. [John Nunn]. In Benko's problem although the removal of the wQ was paradoxical, it wasn't so surprising, especially once I saw how so many attempts to use her to deliver checkmate failed due to the many guards around the bK.
Puzzle No. 3: There are two solutions, so it looks like White should castle kingside in one solution and queenside in the other. I looked for such solutions but (initially) failed. However, the mischievous comment "... one of the problems contains a very clever subtlety ..." got me thinking a bit more carefully, and it didn't take long to notice (and prove) that White's last move must have been with the king, hence he can't castle! Still, it was fun to look for the trap solutions that HAD to be there. It's interesting that the directions the bK moves after the captures on e2 are switched between the trap and actual solutions. Moreover, the "symmetric" knight captures (a3 vs. h3) and different blocks on e4 leading to reasonably different checkmating positions are fairly pleasing.
Puzzle No. 4: I remembered seeing this problem in "Solving in Style" but fortunately couldn't remember anything about the actual solution. Mates in the corner are tempting and "close," but the tempos don't work out. There are set mates like 1...Kd3 2.Nc3 Kc2 3.Na2 Nb3# or 1...Rd2 2.Nc3+ Ke1 3.Nb1 Ra2#, but none of these lead to the actual solution as there's nowhere for Black to lose a move. Given that, it seems reasonable to let the bK make some moves. An idea that just "barely" fails is shown by 1.Kb2 Nd3+ 2.Kc2 Rb1 3.Nc3+ Rb2#?? which fails only because Black's Nc3 delivers check. The simplest way to use the bN without delivering an annoying check is to let the bK run all the way to it. This leads to the actual solution with a surprise midboard mate.
Puzzle No. 5: Given how fond you are of posing problems to Garry Kasparov (and how happy you are to note when he fails to solve them), I'll guess that he's the one who lost the wagers, though I could of course be way off base here.
For the Benko Easter puzzles we offered our readers a prize. The winner was drawn by chance from all readers who submited solutions, with one condition: at least two of them had to be correct. It was a prize for participation, and here's what the lucky winner gets:
The prize was won by Roland Kensdale of Ellon, Scotland. It is a historical Fritz 11 program signed by Vishy Anand, Vladimir Kramnik, Viktor Korchnoi and Pal Benko's compatriot Judit Polgar.
A special (unannounced) prize of the latest Hiarcs 13 program will be sent to Joshua Green of Laurel, MD, USA, for his excellent solutions, not just in this competition but also the ones submitted for our Christmas Puzzles last December.
Grandmaster Pal Benko is a chess legend: A challenger for the World Championship, an innovator of many modern opening systems, a problem composer par excellence, and a father figure to his close friend Bobby Fischer, Benko has played and defeated most of the top players of the last fifty years.
This biography is a celebration of a great man's creative legacy. Its amazing collection of 138 deeply annotated games which have been carefully prepared to be entertaining, enlightening, and instructive is brought to life by Benko's memoirs of his early years in war-torn Hungary, a world of poverty, chaos, pain, and ultimately, personal triumph. His insights into famous grandmasters transform legends into real people with substance and personality, and his reminiscences of famous tournaments take us on a journey through chess history unlike anything that's been published before. Interviews with note players offer insights into Benko's nature. A massive survey of Benko's openings shows us the scope of his theoretical contributions to the game. Photos abound, and 300 of Benko's chess compositions allow lovers of the game to become intimately acquainted with a strikingly beautiful aspect of chess that most have overlooked.
This highly entertaining and instructive book gives competitors who wish to improve their playing strength a dynamic, fun way to deepen their knowledge and understanding. Available at the London Chess Center