Mostly Harmless

John Alderson's Blog
Tuesday Mar 20, 2007

Incisive Thinking

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Continued from here

Donna is importunate: "I've got the last piece, does that mean I get a prize then?". Ursula attempts to smoulder but technical types are unconvincing smoulderers.

"It's the person who puts the last piece in who gets the prize, not the person who's holding some random leftover piece."

"Alright then," says Donna, meeting Ursula's gaze levelly, and with one deft movement she removes a piece from the puzzle and replaces it with the spare. She seems to have made a good choice because it is immediately impossible to say for sure which piece has been exchanged. "Ah, that'll be the last piece then," she smirks, "This one wasn't a good fit."

"Let me have a go," says Ursula and, as Donna obligingly passes her the piece, you might be forgiven for thinking Ursula was already intending to snatch it. She stands over the puzzle, peering at the piece and muttering, as though it were some more than usually delinquent doubly linked list. But the new spare piece refuses to be re-homed.

Risto "I-am-not-a-Finn" Kymmentäkivi - he who is always running tomorrow night's build of Solaris and always seems to get the best chair in a crowded room - sits back in his chair and puts the tips of his fingers together.

"The status of any remaining piece is difficult to determine. There may be still be an error in the puzzle. I mean, let's list the possibilities:

  1. The remaining piece could be from some other puzzle - maybe even another Pollock - or it could just be a duplicate. Either way it can be discarded.
  2. The remaining piece could be a genuine missing part of this puzzle which has been ousted by a foreign piece or one of a pair of duplicates which is currently in the puzzle. In this case we should find the rogue piece and evict it."

"How do we do that?" says Ursula looking up blearily.

"Well, if it is itself a duplicate then we can simply compare it to every other piece in the puzzle. But that doesn't help if some other piece is duplicated or if the rogue piece is from some other puzzle. Plus it's non-optimal to look at every piece. Probably we should create a subset of all pieces with the same shape and then search within the subset for the best fit."

If there is such a thing as a silent groan then Project Central is resounding with it at this moment. Donna is rolling her eyes and seems about to protest when Risto continues, "We can probably automate the process by breaking the puzzle into sections small enough to photocopy. If we photocopy the reverse side then I can get some pattern recognition software off the web to hunt down the candidate pieces. I mean, it's a slog but we don't want to put a picture up which might have a bug in it..."

So the puzzle is carefully dismembered into about eight A3-size pieces and a curious cortège of assorted engineers and onlookers (stifling giggles) makes it's way to the photocopier/printer area. Donna has a somewhat stooped appearance and is less perky then usual. But then, as the first section is being gingerly slid onto the glass, she adjusts her ponytail and says airily to Ursula, "Hang on, can I see that piece again?" Ursula hands it over.

"You seen somewhere else it fits?"

"Not really. I was just thinking, why don't we ... I mean I just thought of a way, right, that we could further optimize this procedure."

And, again, rather too quickly for anyone to stop her, she pops the piece into the gaping jaws of a shredder and presses the start button. She turns back to the stunned crowd (now numbering about two dozen people) and, looking radiant, exclaims "Does that mean I put the last piece in?"

After the cheering dies down it turns out some folk are somewhat peeved by this turn of events (I think you could probably name a couple) but to my mind it puts Donna on a podium with Alexander The Great for sheer schutzpah if nothing else.

* * *

Later that day I find Risto loitering in the photocopier/printer area. He seems a little distracted.

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