Listener 4151: Number or Nummer by Ruslan

[midazolam]

Tricky start to this numerical with a preamble that initially confused me as I misunderstood what was going to be English and German.

I now have all the letters, a completed left hand grid and the two words, but yet to determine the right hand grid.

Will sleep on it

[trux]

CaptainC : welcome ! and I am afraid yours is the first path that I was forced to abandon .... so, nein Mein Herr ... (and let me be first to offer thanks to TB69 to suggest that there might be some glimmer of hope for us all to understand the instructions correctly, if still not any to solve the damned thing which has already given me much KATZENJAMMER)

[jim360]

Could number solutions clash when the letters don't, e.g. if the across answer for a cell gave a 3 and the down answer a 2 for the same cell, that would end up as T in both cases?

That would certainly solve the problem I'm having matching 15d and 24ac, using the b*d*d rule...

[fyellin]

Jim360: You are correct. The letters have to match, not the numbers. If a square contains a Z, it might be an answer written in English with a 0 in that spot, or an answer written in German with a 2 in that spot, or both.

When the instruction says there are two solutions, it is being quite literal. There are two different assignments of values to letters that let the grid be filled in. Don't fight it.

[jim360]

Thanks fyellin. I started following that line and it's led me to nine "possible" pairs of values for b and d (I dare say more clues will help filter that down). I think I can make some progress now I understand how the puzzle works!

[TheBear69]

In starting this out I noticed that D^2 had an even ten's digit for any of the primes and then I wrote code to test the idea and this seems to be true for all primes at least to 37181...Anybody know why? Is this a known theorem?

[B0dger]

Well I can confirm it all works out nicely, that there are precisely two solutions and that a career in IT is not entirely wasted. Anyone else out there who found the better challenge was to write a program to solve it?

[dsmarley]

Thank you for the confirmation, Bear! I decided to start over from scratch as I noticed a way to narrow two variables to about a dozen possibilities and I thought that'd be a good place to restart from. I worked methodically through about half the possible combinations before hitting on both solutions, and I see now what was wrong with my near miss. I may or may not work through the remaining combinations tomorrow just to see for myself that there are no further solutions.

I had considered writing a simple BASIC program to chug through the 10! combinations and tell me which gave answers with the right numbers of digits for all clues. I didn't, but now I sort of wish I had.

[TheBear69]

Actually it's easy to prove that p^2 has an even ten's digit for all primes; p^2 has even tens digit for any odd number whether prime or not:

1^2 = 1 so tens digit = 0
3^2 = 9 ditto
5^2 = 25, tens digit = 2
7^2 = 49, tens digit = 4
9^2 = 81, tens digit = 8

Any other odd number, k, = 10n + o where o is the unit digit.
k^2 = 100n^2 + 20no + o^2
All three of the addends have an even tens digit.

Similarly squares of numbers ending in 0 or 2 or 8 have even tens digit and squares of numbers ending in 4 or 6 have an odd tens digit.

[contendo]

It's all a long way from anagrams and hidden words.

[midazolam]

The fresh light of another day and i have finally cracked it.

I made a mistake in the right hand grid despite being able to fully complete the right hand side of it. Probably ended up with the same mistake as you bassoonery when the left hand side of the right grid failed to work.

On one side of the coin it is clever that there are 2 solutions, but the second side was too much of a drawn out process to be enjoyable, although that might be because i made so many errors.

[Clamzy]

Last week a cryptic preamble and this week an almost incomprehensible one. Fortunately we have our very own interpreter:-)

On Friday I had the same bottom right corner problems mentioned above but once I switched to entering letters it was an easy Saturday finish.

[LiEmers]

Am I correct in assuming that when filling in the right hand grid none of the numbers will be numbers already used in the left hand grid?

[IainGrace]

Good luck this week. Not for us.

[silversolver]

Phew, finally got there. That was a bit of a slog - I spent a long time working out how to get started and nearly gave up but perseverence eventually paid off. I do not generally enjoy the numericals and this one was no exception! Roll on next week and back to the usual format...

[LiEmers]

Resolved my query - it was pure wishful thinking to interpret the instructions in that way!

Unlike most of you, I enjoy the numericals and they are my only foray into Listener world - back to the jumbos for me next week!

[tristram37]

I normally try and generally manage to complete the numericals; but posts to date suggest that this one is a slog too far and I have therefore abandoned it.

Tristram37

[Cruncher]

Home straight now. There was an awful sinking realisation as I completed the left-hand grid and enjoyed the little PDM of the hidden words that I now had to start all over again with no bonne bouche to look forward. Bit of a slog with the calculator

[jim360]

I think I might actually have solved both the grids by now. Wish someone could help me check my working... but at any rate I'm not sure what to do now I've finished both grids.

The preamble says that "Solvers must identify the English transcriptions of the answers entered using German in one of the grids, which, in clue order, form two words of equal length that are to be entered below the grids...". What does that even mean?

[jim360]

Never mind... I should have just thought about it a bit more. Got the two words now. Leaving just the simple question: "Is clue order across then down or by increasing number? That is, would 10 across come before or after 9 down?"

I think that's only the second time I've ever completed a listener - mainly because I never understand the word ones.

[tilbee]

Didn't take my own advice and actually started out on this numerical. Thought I was making progress until I came to an inconsistency and realised that I would have to start again.

My total admiration for anyone who solved this using basic tools such as logic, paper and calculator. For anyone who solved this via computer programmes, respect but not sure that this is what is intended.

In the absence of any personal success this week, I hope you will forgive me in my vicarious pride in my twin nephews:

http://www.telegraph....st-2011.html?image=36

At least I know the next generation is brighter than me !