Listener 4010: Euclid's Algorithm by Aedites

[midazolam]

Here is the link to the numerical listener crossword

[Walterloo]

I do have to agree with one of Lordbadger's comments, in regards to these number ones spoiling a run of correct normal entries. That is exactly what this one is going to do. That, to me, is frustrating. Why can't a number puzzle be printed either with a normal listener alongside, or be 'numbered' differently i.e this should be Listener Mathematical No 86 or whatever, and number 4010 be next weeks word puzzle. I don't mind having a week's break from Listener solving and I'm all for still having the mathematicals for those people that do them and enjoy them, for which envy and respect from myself is duly given.

[cluelessJoe]

I'm wading through it, but found this page useful for getting me started ....

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

cheers

[Cruncher]

I'm slightly embarrassed to say that I enjoyed this one. I took a wrong turning yesterday and started again from scratch today and had more fun cracking the early entries than the rather routine grid-filling at the end - but all in all good for the brain cells and an enjoyable way to spend a wet grey Sunday. It would take me longer to create a spreadsheet so I got there with a piece of paper and a rudimentary calculator and little bit of deduction. Take it bit by bit Walterloo and that all-correct run may yet be intact.

[cluelessJoe]

Just about sums it up Cruncher - enjoyable up to cracking the early entries ... thereafter I'm afraid it becomes a very tedious exercise in grid-filling offering very little more in the way of satisfaction.
Never mind, back to something more normal next week

[x_word_fan]

Clamzy
Either your last digit in Y is wrong or you have a wrong value for f .

As an ex maths teacher who only sometimes finishes the ordinary Listener - the Mathspuzzles are the onesI look forward to.

[Clamzy]

x_word_fan
I didn't say what my value was for the final digit in Y so I don't know how you conclude it's wrong.
As for the "f inZ" didn't you notice the smiley? If you look through all the hcf values for Z clues you will see that there is no f.

[x_word_fan]

Not really clear what you were originally asking then. I have a completed grid which all checks out - what do you need to know?

[AHearer]

It seems to me that Cruncher and cluelessJoe have summed this one up really well. As for the Clamzy/x_word_fan exchanges, they just shows why several of us don't relish the numerical puzzles: too much mechanical decuction causes the humour circuits to atrophy.

For what it's worth, the last digit in Y was the first digit I entered, and I'd guess this was where most of us started.

[MartianAlien]

But beermagnet I don't understand your statement:
There are 22 primes between 2 and 79 inclusive - they are indicated by lowercase a through w
22 primes imply a thru' v. w would be the 23rd prime ie 83.
Where am I going wrong using 23 primes, 2 to 83 inclusive?

[midazolam]

there are 22 primes (2-79 inclusive) these apart from 3 are also the lower case letters a to w (not including i j o and q) =19.
therefore 3 of the primes are not represented as the lower case letters

i much prefer numericals that have some sort of letter transformation at the end (as we have had in the last half dozen or so numericals)

[MartianAlien]

Sorry midazolam
I must be extremely thick because I do not understand your reply.
There are 22 primes: 2 - 79, which would normally be "a" to "v", and NOT "a" to "w".
How do you get 19 primes (ignoring i, j o and q)?
Patience, please - I'm determined to solve one of these wretched mathematical "puzzles"

[bonefixer]

MartianAlien - don't worry about what lowercase letters are used - they're not actually relevant. Of the 22 primes between 2 and 79 only 19 appear in the clues, as presumably the other 3 are never a common factor in any intersecting radial/circumferential clue. The setter uses the letters a - w, omitting i,j,o,q - presumably because these get confused with 1,1,0,9 if your handwriting is as scrawly as mine.

For all those moaning about the quarterly numerical listener, there are a few like me who can never even start the word puzzles and look forward to the quarterly dose of arithmetic. Every other Saturday I just stick to the regular crossword.

[Cruncher]

Hi MartianAlien

There are 23 letters from a to w in the alphabet although, if you read through the clues, you will notice that four of those letters do not appear, so only 19 letters are used.

There are indeed 22 primes from 2 to 79 of which 19 are defined by the lower case letters. I can't honestly remember whether the other 3 primes are used in the grid - they may be - but as they never appear as common factors between intersecting entries they don't require a letter.

As to whether there is any signifcance behind the correspondence of letters and primes, and thus of the omitted letters, I can't say. I could have checked but I took my dog to the pub instead.

Good luck!

[MartianAlien]

So Cruncher, you're saying I do not need to evaluate the clues? So how can they help?
I have assumed to start cell Y17 I need to evaluate "fnt", which I think is 39689.
Obviously up a creek here!
I think I'll give up and go back to last week's.

[midazolam]

a-w = 23 however if you scan the clues 4 letters are not there

23-4=19

therefore only 19 of the 22 primes (2-79) are represented as the lower case letters

if you look at Y then you can see that it must contain at least 6 primes (lower case letters). There is one other entry that contains 6 primes. From this you can work out which primes factorised can lead to these 2 answers

hope that helps - but that is only the beginning!

[MartianAlien]

Thank you midazolam.
I'm sure I don't deserve the help, but a faint glimmer has appeared!
Thanks

[MartianAlien]

... except any 5-digit number from 6 factors means it ends in 0. How do I then get a similar number (ending in 0) from 4 factors, for spoke 18?

[bonefixer]

If a number contains the prime factors 2 and 5 it must end in 0 (and the converse is also true)

Given that Y has 6 factors, you can work out what some of them are. For example, one of its factors must be a 2, because 3x5x7x11x13x17 (the smallest 6 factored number without a 2) is greater than 99999. Carry on with the same logic, and take it from there.

[jamesah]

Glad that's over for another 3 months. Did anyone else find thr preamble confusing? It seemed to say that each hcf was a product of primes which wasn't the case at all.
Perhaps I just misread it.

[MartianAlien]

OK, one final whinge and then 'll return to where I belong - and it aint Venus!
Y (aflnrt) and 17(fkntuw) both have 6 factors, but between them it is 9 different factors: a,f,k,l,n,r,t,u and w.
For any entry with 6 factors it must contain the first 5 primes followed by 1 of primes 6 to 12.
I'm wrong somewhere, obviously.