c4countdown

ENMASKED is listed as valid on Apterous. Sigh.
It is valid indeed. ENMASK an alternative spelling of INMASK, but the search bar doesn't find ENMASKED. Susie should always check the non-inflected word.

I don't understand this at all - if you've spent even a little bit of time on the ODO since its ...

Which ones give the best average solvability across all sets of 4 (so for example 12 has 88.28% with 16, 18, 24, 91.76% with 37, 62, 87, etc. and then taking the average of these)? Was what I was originally thinking, though you've answered an equally interesting question anyway.

In that case ...

Which large numbers are generally most useful, across all combinations with other numbers, and which are least useful? 97 and 12 respectively?

Nope. The most useful numbers, in order (some omissions) are:

11, 13, 12, 14, 17, ... , 92, 90, 98, 96, 100

97 comes in 15th from bottom. As you can see ...

By the way, if you're only playing 4L, the best possible set of large numbers is 12, 14, 17, 57, with 49,438 / 49,445 (99.99%) of games solvable - only 7 games not solvable!

The unsolvable games are:

12, 14, 17, 57, 1, 1 ---> 344
12, 14, 17, 57, 1, 1 ---> 381
12, 14, 17, 57, 1, 1 ---> 423
12, 14 ...

Where do 12, 37, 62, 87 fall?
2 prime numbers, and 62 having 31 (a prime greater than 10) as a factor should put it much higher than the default.

87 = 3*29, but anyway...

12, 37, 62, 87 comes 1,810,325th out of 2,555,190 (30th percentile, so worse than 97, 98, 99, 100) with a breakdown as ...

Great topic, enjoyed reading all this!

Harder question: if one were designing a new variant, which four large numbers (in the range 11-100) make the game hardest (i.e. fewest games solvable) and which easiest (i.e. most games solvable)?

I have an answer for you, Charlie. The easiest four numbers ...

Johnny Canuck wrote:Tim's route to 220 is not the one I would have ever thought to take...

Obviously you saw (100 * 50 + 75) / 25 + 10 + 7, right?

Ian Volante wrote:

Dave Ricesky wrote:you can reach values larger than 2^31

Really? How, given that 25*50*75*100*10*10 is under 1x10^9 and 2^31 is >2x10^9? Some intermediate factoring steps?

Charlie's question was about using different sets of large numbers - and 100*99*98*97*10*10 is way too big, for example.

Just an update on Charlie's question - I've got full statistics for how many 0,1,2 or 3 large games are gettable with each possible set of large numbers. I was expecting to be completely done on the 4L by now as well, but my program hit a snag after I kicked it off and I didn't notice until now. For ...

Dave Ricesky wrote:Charlie, I'll be able to answer that question restricted only to 4L picks in the next few days. Over all picks 6S to 4L, it seems to me to be intractable to get a complete answer at the moment.

Changed my mind. I can answer the whole thing within the next week, probably.

I'm okay with an imperfect answer, I'm sure we can get somewhere with a bit of stochastic hill climbing or some such. (I haven't tried this myself yet but it would make an interesting contest I reckon.)

Hill climbing methods don't seem directly applicable here, since everything in sight is ...

I'm okay with an imperfect answer, I'm sure we can get somewhere with a bit of stochastic hill climbing or some such. (I haven't tried this myself yet but it would make an interesting contest I reckon.)

Hill climbing methods don't seem directly applicable here, since everything in sight is ...

Charlie, I'll be able to answer that question restricted only to 4L picks in the next few days. Over all picks 6S to 4L, it seems to me to be intractable to get a complete answer at the moment.

3rd numbers alt: (25 * 50 + 6) * 75 / 100 = 942

Excellent, dramatic game, although I'm unclear on the rationale behind going for 2 large in the final numbers game. If you're "relying on the conundrum" anyway, why not try for a trickier numbers game - then, even if you don't get it and your opponent does, you can "rely on the conundrum" to win ...

Shame Giles didn't take the chance to embarrass Nick a little when he made a remark along the lines of "I bet you both have the same word" after both contestants declared 9.

Excellent, dramatic game, although I'm unclear on the rationale behind going for 2 large in the final numbers game. If you're ...

Jon, how long does your program take to solve all the numbers games? I've dug up my old code (and made a couple of tweaks) and it can chow through all the standard numbers games, including recording an optimal* solution to each one, in a matter of minutes.
That's mightily impressive - is there any ...

Alan Rickman dies aged 69

http://www.bbc.co.uk/news/entertainment-arts-35313604

But sometimes these alternatives don't exist. What numbers solution requires the highest intermediate solution?

I'm afraid that's one question I can't answer without significantly slowing down my solver - some optimisations I've made to it mean that it discards quite a lot of potential solutions ...

-

-

Since you asked so nicely, you're on! Running now, so hopefully should have some results tomorrow...

Jon, how long does your program take to solve all the numbers games? I've dug up my old code (and made a couple of tweaks) and it can chow through all the standard numbers games, including ...

Yep, that agrees with the rough memory I had from ~2 years ago when I did this myself. I don't remember 2 or 4 large being quite so similar to 3 large in terms of gettable targets, but my overall surprise at Nasty 3 large being THE most gettable numbers variant probably just dulled my memory of the ...

Jon, I think you should do a similar analysis on the solvability of numbers games with the "nasty" large numbers as used in a couple of special episodes (those larges are 12, 37, 62, 87). I've done that analysis in the past and there's something very obviously surprising about the results when ...

Gavin Chipper wrote:FECKER was there as an alternative Callum beater (though not the max) in round 10.

Or HEIFER, or even CHIEFER (if there's still a one syllable rule).

SPEARGUN coming up was clearly a bad omen for George (cf. Episode 6054, his other loss)