## Friday, December 19, 2008

### Euclid's calculator-button mashing

We're on to the last numerical puzzle of the year, and it's something I haven't seen before, a circular numerical puzzle. Aedites has given us one circular puzzle this year (the first circular I had ever solved), and after my boast earlier in the year that I can usually do numerical puzzles, I have only finished one of the three (and I didn't get Big Holes either).

First thing, I thought something had gone wrong with my printer when it spewed page after page and most of them looked blank. When I print off the Listener, I usually limit it to two pages (I print on American letter size paper, so it's a bit shorter than A4), but since numericals typically have fewer clues, I didn't bother. And here come the pages!

All entries are 5-digit integers who only have single prime factors 2-79, no factors repeated. Intriguing... trying to do them from memory, I write down the primes from 2-79 and completely miss 41. I'm off to a great start...

Each clue is the common factors, if there are none, there's no clue. Intriguing... so next step is to write out the list of definite factors for each letter and each number. This may not give all the factors (in fact in 24 and C it appears there's no factors in common with anything), but it gives some juicy starting points. I know some have six factors...

Y = f a r t n l (heh, fart)
17 = f t w n k u (heh, ftw)

A bit of poking and prodding on the calculator shows that there has to be 2, 3, 5 present to have six prime factors and still be a five-digit integer. So several pieces of good news... f, t and n have to be 2, 3, and 5. Anything with these three factors is going to end in 0 (multiple of 30), so I can confidently write in a 0 at the end of anything that has f, n, t as factors. Which is only T and Y (and 17-21 that cross Y), and 30. Three whole numbers in the grid!

Now 19 doesn't have f as a factor - so f has to be 3 (otherwise it couldn't end in 0). One of n and t is 2, the other is 5.

So let's see - the five digits of Y...

first digit crosses 1-4 which have n but not t
second digit crosses 5-8 which has neither n nor t
third digit crosses 9-12 which has t but not n
fourth digit crosses 13-16 which has neither n nor t
fifth digit is 0

So look for combinations of those last three factors that give a number that goes...

even - odd - five - odd - zero

or

five - odd - even - odd - zero

30 x 7, 13, 19 gives 51870, but that won't work as 30 x 11, 23, 29 is out of range for 17

30 x 11, 13, 19 gives 81510 for Y, so that makes 17 30 x 7, 17, 23 = 82110 and we have our first two full numbers in!

This means n is 2 and t is 5, so any entry with t in it ends in 5. l a and r are 11, 13, 19 and w, k u are 7, 17 and 19.

Z now looks like -50-5 and has factors l,a,r (don't know what they are but know what they come to as a product), t and k, so 13585,w means w = 7 and the entry is 95095.

And we are off! Most of these were filled by getting the known factors and looking for multiples that worked with the numbers that I knew. I only used the "cross-checking" of making sure the remaining factors didn't cross a few times, notably in getting C (factors of 29, 31, 37).

This was a single-sitting solve, rare for me. Didn't check the time, but it clocked in at a few hours of hunting and pecking. I didn't use a spreadsheet, but I used one of those dinky old calculators that will repeat the last function if you press equals. I'm glad it printed on four sheets, I actually needed to spill over to a fifth to get all of my notes in. Here's how things looked at the end...

What looked like a daunting prospect turned out to be a pretty nice exercise in logic and patience - I had fun with this one. And a victory to George! With just a few crosswords left in the year I've stuck my neck out again, one more completion guarantees me at least a draw.

Current tally: George 24, Listener 22. Current streak: George 3.

If you're doing the holiday thing, have a safe and drunk one! I'll be in Houston next Friday, I'll have internet so I should be able to do the blog, but I may not have any images up, taking the scanner on the plane sounds like a bad idea.

Duncan said...

Good job. I couldn't get into this one, oddly, as it ought to be right up my alley.

I must say I have enjoyed your blog over the year. It is most reassuring to share the struggles with someone else rather than the elite who populate the other sites. I really hope you carry on through 2009, now that you are in the swing of it!

Merry Christmas

George the Bastard said...

Thanks, and thanks for all the comments. I'll keep things going (I even have the same block of Friday in my day schedule) for the next year. I probably should set the bar a little higher, maybe not allow myself a bit of leniency. We'll see - hope you have a great time.

I had what should have been a two-hour plane trip to Houston turn into a five-hour happy fun day with Homeland Security and the random Texas weather. I was well-equipped for delays, as I had...

Mephisto 2521 (nearly finished)
Azed's Christmas puzzle (finished)
Auracuria's Christmas jigsaw puzzle (missing two entries)
Sunday Times Jumbo (started, then found either the grid or entries were wrong, grrrrr)
Anax's Imperator puzzles 1 and 2 (they're linked from the Times for the Times page) - got less than half the clues on 1, all but about 5 on 2
Bandmaster's Tribute to CJM puzzle (linked from the Crossword Club page), which I was just getting started when we touched down.
Listener 4013 was next up if needed

Sitting across the aisle from me was a woman who had printed the Sunday New York Times and completed about two-thirds of it over the trip. She was getting a kick out of seeing what puzzles I had.

Longest comment ever!