To all BBC CiNA Calendar Puzzle 2010 Owners
The September competition with grid and clues set by Bud was won by Bill and Marilyn Gabbett. Paddy O’Connell (Radio 4 Sunday 9 am ‘BH’) was kind to conduct the virtual draw.
The ‘Victorian Hedge’ clipped a couple of excellent solvers from the World Championship with just twenty moving forward with 100% records to the fresh challenges of October. I am afraid I had to be dragged out backwards.
Looking ahead to next year I would be most grateful for your reflections on the project. Several solvers have provided encouraging feedback during the previous months. These and more critical comment from friends would be invaluable for planning.
I was delighted to see that Nora Boswell who achieved a splendid second place in the 3D world competition last year, came up trumps again in the GU September Genius crossword set by Lavatch. James Brydon’s puzzle constructions are quite outstanding. The same might be true of his clues if only I could do them. The grid was based on a thought provoking principle. The answers to some of the clues had to be moved up or down the alphabet to fit into the grid. This was a little like having two grids where there is a rule that connects them. That led to some apparently delirious thoughts which I append below. I will spare you them here but some conclusions are quite astonishing.
An electronic 4D crossword is now easy to construct. A pan-dimensional crossword is quite achievable. (If anyone wanted one!!) Quantum Physics has no fear of particles with over a hundred dimensions. Dimensions in crosswords do not have to be whole numbers. Crosswords can be fine-tuned in difficulty. An electronic crossword (such as the Spoonbill blind crossword) could have various controls that the setter or solver adjusts to produce just the right degree of difficulty.
I wish I’d had a knob to twiddle on the Hedge!
Thank you everyone for continuing to support our project.
Happy, tormented solving,
Releasing Crosswords and Letting Them Fly
The simple principles of crossword construction have governed the way we have solved such puzzles for decades. Within these principles, there is a great deal of room for creativity to exercise both setter and solver alike. Nevertheless, it is worthwhile to look at those principles and the assumptions underlying them. Who knows what might be possible if we started to interrogate them?
Crosswords work by the solution to one clue giving letters in other solutions that the first one crosses. The assumption is that the solutions have a letter in common where they cross. That seems obvious. But let’s look at that assumption.
The important thing is that there is a correspondence between the letter in a square from one solution and the letter in the same square from another solution. That seems to be saying the same thing. It is saying the same thing, but only if the correspondence is one to one.
But what if instead of there being the same letter shared, there were a rule connecting the two letters, each from a different solution? Lavatch, for example, does this in the very entertaining September GU Genius puzzle. To make it possible to work out ‘the other letter’ and to avoid the complication of writing two different letters in the same square, there is a rule for converting the letter from one solution to make it the same as the other letter. On paper crosswords it probably works best if the rule is the same for each cross-over - although this does not need to be the case.
The underlying principle is that the letter in a shared square can be used to work out the letter of another solution in the same square, and vice versa. The rule usually is that they are the same letter. But any rule of substitution will work.
There is an assumption of reversibility. If One Across helps One Down, then One Down helps One Across. The puzzle would be much harder if Across helped Down but Down did not help Across. But that is nonsense isn’t it? As soon as you write on the paper grid the solution to One Across you see the letters helping the Down clues. Don’t you???
At the beginning, most puzzles have empty grids. A solver might scroll the clues until a clue is cracked. This gives letters in other solutions and focus moves to their clues. This continues until the puzzle is completely solved, or in my more usual case, until deadlock is reached. A corner of the grid has no letters to help solve the impenetrable clues. In a weekly or monthly competition puzzle, a good (or bad) night’s sleep can produce fresh thinking the next day and the puzzle moves on. This can be satisfactory but sometimes it is too slow for optimum enjoyment.
A desperate solver, stuck in a corner without any letters, could have a “Beam me up Scottie” moment in a three dimensional crossword grid. In 3D there is extra help. Letters in a particular solution are shared with two sets of other solutions instead of just one set. The desperate solver in the 2D corner might be relieved by the joyous sight of a letter hurtling down from the third dimension. Now the puzzle is alive again. There are more letters to help. The solver is off again, finding all that buried treasure that the setter left for us to find.
The extra dimension makes the puzzle easier for a given degree of difficulty in the clues. A 3D setter uses this fact and can employ harder or more imaginative clues than might otherwise be let loose on a suspecting public. There are very few actual 3D crosswords around but if you Google ‘3D Crosswords’ you will find a charitable website where such puzzles can be downloaded freely, on Google Page One Item One.
Optimum enjoyment depends on a range of factors the settings of which are different for different people. This is clearly why a quick crossword in The Sun can co-exist with a slightly longer Listener. Different crosswords have different client groups. Solvers drift and find puzzles which satisfy. They should be challenging but not too difficult and not too easy either. Regular solvers might start drifting ‘upwards’ and graduate to more imaginative puzzles. It should be said that this does not always come with increasing difficulty. Enjoyment has many facets. An easy clue can be absolutely delightful: Araucaria’s “Of,of,of,of,of,of,of,of,of,of” (10) l makes me smile oftentimes. A hard clue can be so dry and boring that it puts one to sleep. The point here is that difficulty can be tuned. This is achieved by the style of puzzle, the clueing, vocabulary and obfuscation. Crossword compilers and their editors build up a wealth of experience to be able to judge such things.
There is an assumption that once the puzzle is put together, the difficulty is set and cannot be changed. Of course team cross-wording changes the balance between setter and solver and can lead to quick-fire solving that has an excitement of its own. Group solving can be co-operative with a competitive edge. Some interactive on-line puzzles have ‘cheat’ buttons to help the solver to keep moving along.
I have been working this year on electronic blind crosswords. In these electronic versions of standard 2D crosswords, it is not necessary to see the grid. It is there. You can see it if you need to and have the physical facility. But you do not need to see it if you do not. The program presents the same information that the grid gives to a sighted solver. For instance, the program will present all the clues for solutions which have been given a letter by another solution. A blind solver can progress through a puzzle in much the same way as a sighted solver. She/he can scroll through the clues in any order of choice or pick out a route determined by finding clues helped by previous solutions.
If the grid were put on one side or temporarily demoted to the status bar, we now have a puzzle presented entirely through text on screen or the spoken word. It faithfully reports on progress in the grid.
Now let’s look at all those assumptions painfully pointed out earlier and to no apparent purpose. In an electronic crossword we have a means of presenting the puzzle that does not require paper. We can try out a few things.
We can make the puzzle harder. Solutions of Across clues donate letters to Down solutions and these are reported but we can stop reports of Down solutions helping Across. This seems very unfair to a blind solver and we run the risk of prosecution under the Disability Discrimination in Crosswords Act. But it is only an illustration.
Do we need one-to-one correspondence between cross-over letters from Across and Down? The surprising answer now is that we do not.
What is important is that upon the solution of an Across clue, a given number of letters are ‘released’ or revealed in the partial solutions of the various affected Down clues. The relationship between two cross-over letters can be anything at all as long as the program holds this information. When a correct solution is entered, the program supplies a correct letter in another solution from an unsolved clue. If an incorrect solution is entered, the program applies the same rule and reveals an incorrect letter.
The number of letters released can be controlled. So far these have always been the cross-over letters in shared squares. The number of letters released can be less, as above, or it could be more as in a 3D puzzle. We can have as many sets of solutions as we like. Across, Down, Away, Trans-cube, Pink, Lucy-in-the-Sky-with-Diamonds…..
If we decide to release more and more letters for one solution we can produce 4D crosswords, or, in fact, any number of D, even a 1.5D!! All that is required is a rule connecting cross-over squares. That might sound complex, but the solver would never see any of this. Compared to the world of quantum harmonic oscillators, a 16d crossword is easy peasy.
Furthermore, if you are still there, the letter released does not have to be one in a shared square. It can be anywhere in any solution of an unsolved clue, in any grid, in any Universe …... This could be controlled according to a number of criteria. Do you prefer to have a starting letter or an ‘E’ in the middle? How about giving preference to a ‘Z’ instead of an ‘S’?
We are now controlling the degree of difficulty of the puzzle for the solver. Let’s look at something for the setter.
What happens if we dare to ask ourselves the question:
“Do we need a grid?”
The surprising answer is “No! Not any more”
All we require is that upon solution of a clue, a controlled number of letters are revealed in a controlled number of solutions of unsolved clues.
A themed crossword always involves a compromise between the words that the setter would like to include, and the forced “fillers” that have little to do with the theme but are necessary to complete the grid. “OKAPI” has tested the most resourceful 2D setters to clue it without repetition. “ENEMA” has been employed so many times in 3D grids that many setters are fearful of straying too far from home.
We can now set “crosswords” without a grid and with no restriction enforced by the need to fill it. Any list of words that the setter wishes to clue can be employed. Beautiful but binding symmetries are no longer a restriction.
The term “Crosswords” is placed in inverted commas because the final questions here are to do with whether this is still a crossword??
Whatever it is, we do have complete freedom to set exactly the puzzle we want. We can choose any words we want and we can tune the difficulty of the puzzle, in any number of dimensions, to the nearest micro-cluon.