Listener 4334 By Brimstone

[Contrarian]

Much easier than it first appears, if you know where to start.

Thanks Brimstone.

[Cloverjo]

Atherun, also I don't know if this is ok, but anyway. I don't have my copy with me so can't give the clue number, but start with the one with lots of Fs.

[Oyler]

The first 3 rows in the grid refer to the top layer of the cuboid, the next 3 rows the middle layer and the last 3 rows the bottom layer. They are then stacked on top of each other to make a 3x3x7 cuboid.

Some entries are unclued as you have to work them out once you've solved all the clues using the 'magic' criterion.

Hope that doesn't give too much away.

[jim360]

If people want to ask for hints they can create a separate thread and ask there, following S-D's example from last week.

[perseverer]

Atherun - i will start a separate Hints thread, to try and answer your points.
Cloverjo - It is not a question of being allowed to, it is just that the people who participate in this thread see it as a place for discussing a Listener without too much being disclosed, and ask people who participate in the thread to go along with this. And I don't think you exceeded this with your post.

[Oyler]

You can think of the 3x3x7 cuboid as an elongated Rubik cube.

There is no need to search through all 4096 possibilities with a spreadsheet or program. The preamble sees to that. If you had to do this then the puzzle wouldn't follow the rules that the setters are required to follow. Essentially the puzzle has to be able to be solved using a standard scientific calculator and no more. If you had to search through all 4096 possibilities by hand and doing 1 a minute this would take 68 hours which is far too long to spend. So if a spreadsheet considerably reduces the solving time then the puzzle won't appear.
Of course that doesn't stop solvers from using spreadsheets and the like and throwing everything including the kitchen sink in an attempt to solve the puzzle but those aren't going to be necessary in a Listener numerical.

[doctormatt]

Done: it did need lots of care to avoid transcription errors, but managed to work through it without the dreaded excel sledgehammer. Satisfying when I finally checked and all sums came out identical.

[Oyler]

I should also have added that it was a superb puzzle. A great logical workout. Thanks Brimstone.

[rickyjohn200]

Thanks Cloverjo but I still cannot visualize this. All I can see is a Rubic's cube/ or die but elongated in one direction. In which case you can see the top, bottom and four sides but no three layers.

[upsetter]

Retrieved the toys and finished the puzzle.
But the experience is as predicted - vast amounts of trawling back over errors.

[EAChaplin]

One of the best Listener numericals for some time - thanks Brimstone.

Rickyjohn200 if you lift off the top layer you can see the middle.

Oyler - interested in your statement that Listener numericals should be solvable by calculator and without spreadsheets etc. Last year's Boxes by Radix would no doubt meet your criteria but how long would it have taken? I did ask Radix that very question but didn't get a response. I hadn't realised how ill he was at that time.

[AndrewG-S]

I wonder how this was set, is there some clever way to work out 7 similar magic squares where you can align them to have each row give the same number or does this need computing power - I suspect the latter but would like to know either way. I was probably in retrospect rather too bland in my comment on the puzzle, the more I think about the magic squares, linkage between the 7 squares, square nature of clues and simple elegant finish but which requires some thought the more I think the puzzle was closer to a real masterpiece.

[starwalker]

Thanks Brimstone. I am simply in awe of the construction of this puzzle. No idea how it was done, and not sure that I really want to know. Still a numerophobe, but a very impressed one.

[AWP65]

Its good to see positive comments outnumbering the negative ones at last. This was a truly impressive construction. It seems to me that most contributors to this thread each week should have passed the stage where solving the Listener is a matter of self-congratulation. For experienced solvers, arriving at the solution is almost a certainty. What keeps us doing it week after week is the pleasure we find in original and pleasing clues or in a beautifully constructed puzzle. Here we have a really remarkable example of the numerical kind, and I feel comments expressing dislike of the methods needed to solve it are just as inappropriate as comments expressing a dislike of cryptic clues would be. If you don't like numericals, don't do them!

Thank you Brimstone.

[Cruncher]

Amazing piece of engineering. Not nearly as difficult as it first seemed although it needed a little trial and error to work out the final rotations

[TheBear69]

Rickyjohn200, think of this as a loaf of bread such that if you view it from above you see rows 1-3 and from the bottom you see rows 7-9. The slices of the loaf are the magic squares. E.g. if you label the cells in any column abcdefghi then you get magic square:

abc
def
ghi

[BMACMAC]

A most enjoyable puzzle: thank-you Brimstone. I don't see any reason for not using Excel. It's a good way of recording what I've deduced s that I can easily go back if I reach a contradiction, and at the same time it allows quick and error free evaluation of lengthy expressions, like those in the clues.
I didn't find any dual solutions, but then I followed the constraints in the preamble so presumably I avoided anything that wasn't going to work.

[word_cross]

nice puzzle - Excel definitely not required*. Would have been a quicker solve if i had not got confused with my (different from usual) calculator which resulted in some of my 'squares' being 2x rather than x^2!


*except that I use excel for just about all of my Listener solving to keep track of clues, grid, answers and whatever the week's thematic information is!

[British_Olympics]

Don't think you've gone wrong AHearer. The sum of the numbers in the first 2 cells of rows 1 and 9 of the final grid are the same, and this is also true for rows 2 and 8, 3 and 7, 4 and 6. Therefore rotating slices/columns 3 to 7 by 180 degrees would have given a valid alternative solution without the "It may help to note ..." (which as you say really should read "to distinguish between the 2 possible solutions, solvers should note ..."). In this case, however, the total of the numbers in the cells originally occupied by single-digit numbers is only 150 and 4 of these cells remain unchanged.

[olichant]

A really clever construction - I am in awe that anyone can set puzzles like this. Daunting preamble, to be sure, but not such a bad solve in the end. Like Andrew G-S, I preferred the endgame to the gridfill, but it all came together satisfyingly. I'm not sure I took the most efficient route - I'll be interested to see the published solution.

[AndrewG-S]

For the endgame the information given in the preamble plus two other observations (which admittedly took me about an hour to get to but should have been much quicker) led to a unique solution with no trial and error/spreadsheets etc.