Listener Crossword 4023 - Pentomino Factory by Oyler

[starwalker]

Another week, another thread. This week's Listener is the "dreaded" numbers puzzle, which actually looks like it might be fun.

[Philoctetes]

Oh the frustrations of no Friday night grid. But the chance to ask (without knowing what is coming) how others go about approaching the numericals. Are there any standard first steps, or is it just stare at the clues blankly until something leaps out?

[Apache4D]

Boy oh boy, really not looking forward to this one.........I'll need all the time I can get. Have never tried the numericals, so sure it will be a challenge.

If there is interest, and no objections, I'd be happy to post the pre-amble for those itching for a headstart!

Otherwise, see you all tomorrow......

[Speravi]

Philoctetes, speaking for myself, yes, examine the clues and look for something that looks "different". As an example, and without, I hope, giving too much away, look at column 9, where the product is 32, i.e. 2 to the power of 5, and ask how that could be "created".

Also, think about the implications of the three rows with a product of zero.

I tend to find myself chipping away at the numerical puzzles, often proceeding by elimination, rather than getting flashes of insight or a penny dropping moment.

[cruciverbali]

A couple of year's ago Derek Arthur produced a User's Guide to the Listener crossword, and Part 4 covered Numerical Puzzles.

[AHearer]

Oh, I do hate the numerical ones. The only thing that immediately leaps out is the position of piece 11, which may help to pare down the 1010 ways of packing this particular shape with pentominoes. As Speravi notes, the 3x3 square of 0s narrows down the number of shapes that 0 might be. I am also attracted by the 2 to the power 5, but a little wary that it might be too obvious: 32 = 2x2x2x2x2=8x4x1x1x1 etc. I think the 5s are helpful.

[Mysterons]

Feel free to post the details Apache. The last appearance of pentominoes that I can recall was Pentad by Tangent in August 2002, so I'm interested to see Oyler's approach to the theme.

[emcee]

Although new to posting I've kept an eye on these threads for a while now ... congratulations on a (generally) friendly environment.

For those who don't like the Listener mathematicals: have a go at this one -- it may seem offputting but, in fact, isn't too bad at all. I proceeded by reducing each clue into a product of primes and began completion of the the grid from the left hand side.

emcee

[Speravi]

Cracked it !

As with alphabetical crosswords, it can be useful to build up an answer. After identifying the positions and shapes of 11, 9, 2, 7 and 10 I had a go at tiling the 5 x 12 grid with what I had. I didn't know whether there would be a unique solution... But thought that if there were multiple solutions then having fixed some tiles in place the number of solutions would be manageable. Having obtained a solution to the tiling problem, I used the column products to conjecture some numbers to associate with the shapes I now had. Obtained a candidate solution, checked it with all the row and column products... it worked.

[easterfool]

Definitely one for those people who are put off by the numerical ones. It does give way easily if you start on the lines already mentioned by Speravi and emcee.
Very enjoyable to maths maniacs like me.
Won't qualify as one of the "Best" crosswords of the year, but it might persuade some of the mathophobes to have a go.

[Apache4D]

Apologies for the delay..........for you early bird's out there here is the pre-amble (Paper is available so hopefully won't upset anyone).

When five equal squares are arranged joined edge to edge the resulting shapes are called pentominoes. There are only twelve fundamentally distinct shapes, when one rules out pentominoes that are equivalent to one of the twelve, through rotation or reflection. Each pentomino has been assigned a number from 0 to 11 inclusive, each having that number present in all five squares. To avoid confusion for grid entry the letters A and B should be used for 10 and 11 respectively.

The grid may be filled exactly with the twelve pentominoes. The clues give the product of the entries in each row and column. Rows are numbered from top to bottom whilst columns are numbered from left to right.

Solvers must enter the correct digits or letters in the relevant squares and the positions of the twelve pentominoes should then be apparent. The pentominoes must be coloured in so that no pentomino touches another of the same colour along an edge or at a corner. Only entries using the lowest possible number of distinct colours will be deemed correct. Any distinguishable colours may be used.

ROW PRODUCT
1 1497375000
2 14701500
3 0
4 0
5 0

COLUMN PRODUCT
1 4356
2 12474
3 15246
4 3150
5 0
6 0
7 0
8 1536
9 32
10 640
11 8640
12 36000

[AHearer]

Yes, definitely one of the easier numerical Listeners. I always feel slightly unsatisfied at the end of these. Whereas the word-based puzzles usually elicit a little smile, or even a chuckle, when the last piece falls into place, it's hard to be witty with numbers (unless you turn them upside down as in the calculator-related puzzles) -- now there's a challenge for the composers.

[Mr Crossy]

Numeric puzzle or not, I always fear the d�nouement that demands spatial awareness. So, how many colours? Can anyone beat 4?

[Mysterons]

Thanks for that Apache - no need to rush out for the paper today !

It sounds like the hardest part of this one will be the colouring - in theory 3 or 4 colours could be sufficient, but we also need to bear in mind that no adjacent points can be the same colour.

[midazolam]

given the fact there are multiple sites out there with all 1010 solutions, they are not required for this challenge, as it is easier to work out the maths first. I started on the right then went to the left filling in the shape for the "0" last.

the amount of colouring we should be keeping under ones hat - as it is not difficult to get the right number of colours.

to answer your Q philoctetes: I always search for the answers that must contain 10, 2 or 5 (ending with 0 or 5), or search for the squares or cubes that are fairly small.

think i will buy the independent today as i do not want to get withdrawal. At least we have another 3 months until the next numerical.

[Mysterons]

......... and a couple of sites that might help with some of the donkey work:

http://www.virtuescience.com/prime-factor-calc ulator.html

http://en.wikipedia.org/wiki/Pentomino

[midazolam]

forget the number 2 in my third paragraph

[Cruncher]

A very gentle stroll. I looked for the 7s and 11s first as they are unambiguous as factors. But it fits together very nicely.

Indeed - a pleasant surprise for the mathsphobes.

[bonefixer]

I only ever do the maths ones, as I find the wordy ones impossible (Times regular crossword is my limit). This maths one is the easiest numerical Listener I've ever come across - solved it without having to use several A4 sheets, computer programming or spreadsheets.

As others have said, factors of 7 or 11 are the place to start, the 0 doesn't come in until the end, and the right hand columns can be factorised, in some cases uniquely. Only 3 colours are required - for those that need 4, try again.

[midazolam]

For anyone who has the independent today, the inquisitor (114) is by Dysart. A regular Listener setter who never fails to produce challenges. This is no exception, a nice theme and a PDM not revealed until the end.

[perseverer]

Being better at maths than spacial awareness - not that that would be difficult - I had hoped/assumed from the first sentence of the last para of the preamble, that if you managed to complete the grid so that row and column products were correct, then this would be the unique solution and automatically generate the pentominoes. Wrong again - I ended up with 2 pentominoes the same. Admittedly a very simple adjustment solved it, but if there is anyone still working on this, beware.