The Parallel Play
This little investigation into the parallel play arose after a small comment made in a Scrabble newsgroup grabbed my attention...
On March 22, 2007, Alistair Kane wrote (in response to a recollection of Harry Malcolm):
... the late Roger Blom once replied to my opening move (which I can't remember)with BOLIXED scoring 116 or something thereabouts, and making 7 2 letter words.
In trying to work out what Alistair's word may have been, I ended up embarking on a much more ambitious project: to identify all possible parallel plays for all (Collins) words of length 2 to 15. Naturally I got the computer to do all the hard work, while I just told it what to do.
I can't think of a concise and interesting way to summarise the hundreds of thousands of results here, so instead, I offer you a couple of snippets in the form of 'problems' (yes, I used to be a maths teacher). I'll hand out the solutions in a few days (yes, I used to be a maths teacher).
But first, let me see if I can help Alistair remember what he played before he was BOLIXED.
Now, Harry claims that BOLIXED was played 'on top of' Alistair's move. So, unless they were playing Upwords, below is a list of all seven-letter words that can potentially be BOLIXED in this way...
If, however, Harry's memory fails him slightly - I mean, he must be really old by now! - and BOLIXED was actually played underneath Alistair's word, here are the new possibilities...
I particularly like the auto-suggestive AWESOME play!
Note that some of the above words (for example, EROTISE and AMADODA) were not acceptable at the time of Roger's play, and hence are unlikely to be Alistair's opening move.
But I'll leave that problem with Alistair now, in favour of some new problems which are much more interesting and even less important.
I was extremely surprised by the large number of parallel plays available for words of length 2 to 9. Indeed, there are over one quarter of a million possible 7-letter parallel plays! The email thread cited earlier, for example, was triggered by a game in which Alistair played HEXENES under UTERINE. It turns out that UTERINE allows over 50 such underplays! I won't bore you with a list - I'm sure you have plenty at home.
So, to make my investigation more interesting, and your task more difficult, I singled out words that only have one possible underplay. Hence your first challenge is ...
Find the only possible parallel underplay for each of the following words...
I then started to wonder how difficult it would be to find words that can be played both over and under another given word, like this...
Again, there were many more solutions to this constraint than I expected.
Hence, your second challenge is...
For each of the following words, find another word that makes a valid parallel play, whether it is placed above or below the given word...
(My computer is still churning away at this problem for wordlengths of 8 and up, so we'll leave things here for now.)
But of course, we are a population driven by cheap superlatives, so what we really want to know is: 'What is the longest possible parallel play?'.
Can we span the full Scrabble board?
Unfortunately, not quite.
The longest possible parallel play is 14 letters long, and there are 5 such solutions (only one of which - the first - was introduced by Collins). Here they are...
Which naturally leads us to your last task ...
What word goes under LOGODAEDALUSES?
Yes, the answer is a word you will know!
And just to complete this little story...
A short while after I made this post, Alistair's memory was jolted and he was able to confirm that the actual parallel play was this one...
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