Constructions past and present January 1st, 2008
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It was one of the nicest phone calls in a long time. The Very Strong Chess Player was on the line, asking about my family, wishing me a Happy New Year's Eve. But soon the primary reason for the call became apparent. "I've been looking at your problems, Fred," said the Very Strong Player. I've solved them all, except one."

Fine, I said, let's go through them. And go through them we did, one by one, leaving out the problematic December 27 position for the time being. We had a great time doing this, since we both love puzzles, and we both love the unconventional and unexpected in chess. And we both have a long history – just over twenty years actually – of swapping unusual mind sport puzzles.

In the end we came to December 27th, where my friend at the other end of the line described the series of moves that led to a helpmate in 22 moves. "Are you absolutely sure it is 21?" he asked. "Yes, definitely," I replied, quickly playing through the solution again to make sure I was not having one of my periodic mental blackouts. "John sent it to me, so it is thoroughly checked." That reassured my partner on the other end of the line.

"But there is no other mate," he said, after some minutes of humming and hawing. "And this mate can only be achieved after 22 moves by Black. I thought about a different mate, but there just isn't any." Being a very astute problem solver he listened carefully for my reaction. None came. "Aha, so there is a different mate?! But where? How? Are you sure?" Silence. Mutterings at the other end of the line. And then: "Oh, dear, how could I not see that! Dear, dear, dear." Except he used a more powerful expletive than the sissy-boy "dear".

I fondly remember our first Christmas Puzzle, back in 1999, where I told the story of the problem to end all problems. This is what it looked like (just one puzzle on Christmas day, I believe):

The puzzle was given to me by (whom else) John Nunn, back in the 80s. He sealed the answer in an envelope and asked me to return this unopened, with the solution written on the back. I passed the problem on to Garry Kasparov and Anatoly Karpov at the time. The saga of what ensued is described on the original page. You can try your hand at it, if you do not know it already. Please do not write in for solutions for a few weeks. We will not give it to you without a fight.

Garry was, as you may have guessed, my New Year's Eve caller. "What are you doing for the New Year's Day puzzle," he asked. "I don't know yet," I confessed, which surprised him somewhat. Weren't these Christmas puzzles prepared months in advance? No, I usually decide a day or two before they are published, going through old collections before I fall asleep. Of course sometimes I have a lot of help. John Nunn has picked the problems for an entire Christmas week in the past, and this time I got help from Richard Saunders, a retired computer programmer from Hampshire, England, who sent me a collection from which most of the positions were taken.

Well, after the lovely interlude on the phone I decided to do another construction problem on the lines of the famous one shown above (but much easier). I do not give the author yet – we want our readers to search for the solution, rather than for the solution on the Internet.

(i) Shortest discovered checkmate
(ii) Shortest perpetual check
(iii) Shortest reflected mate

There are three problems to solve:

1. Find the shortest sequence of moves that lead to a checkmate by discovered check. Naturally both sides are collaborating to try to achieve this goal.
2. Find the shortest sequence of moves after which one side can force a perpetual. In this case both sides cooperate until the position is reached; after that one side has no choice but to accept perpetual. Note that the side delivering perpetual check prefers it to checkmate, which he may also deliver.
3. Black has agreed to play reflected moves as long as this is possible, e.g. 1.e4 e5 2.Nf3 Nf6 3.Nxe5 Nxe4 etc. (so that's where the Petroff comes from!). What is the shortest mate White can deliver if Black faithfully reflects his moves? Note that there are three solutions.

We implore you not to send in any solutions until after January 3rd, when we will have sorted out our mail problem and sent our spammer to the place were all malicious spoilsports go. Solutions to all problems will be supplied next week.

In the meantime we wish all our readers a Very Happy Gregorian Calender Yearly Increment.