If the freedom of speech is taken away then dumb and silent we may be led, like sheep to the slaughter.

- George Washington

Thursday, 16 September 2010

Brain Teaser Solution

OK, I've kept you waiting long enough.

The Omnibombulator:

To get chocolate, you must select switch C.

For the Third Programme, you must select switch D.

Prize for the first (and only) correct answer goes to Endemoniada_88, who wins the desirable, nay covetable, prize of a pint of best wallop if I ever get down his way on my Round Britain Whiz.

Well done that biker!

I did a piece on how it was worked out, including some spreadsheet tables to illustrate, but I can't work out how to get spreadsheety stuff into a Blogger post, so if I work out how, I will. Otherwise, I won't. There's logic.


It looks as though getting spreadsheet data into a blogpost is difficult, so I have cheated and saved the spreadsheet as a series of screen images. Here's my take on how it's worked out:


Unless you are a genius or a chess grand master, you cannot do this in your head.

Start by drawing a 6x4 grid where the six operating conditions can be plotted against the four switch positions.

PV: Pratching valve glows Y/N
QO: Queech obulates Y/N
UC: Urfer curls up Y/N
RH: Rumption gets hot Y/N
SR: Sneeveling rod turns clockwise Y/N
TH: Troglodyser emits hydrogen Y/N

Put in the basic information on the switch positions and you get this:

Now start putting in the additional relationships onto the grid. Keep going back and forth through the various relationships, adding Y or N where you can. I reckon I went through the whole thing four or five times, adding one bit of deduction every time. You are aiming to get either a Y or N in all boxes, but I didn't quite manage that. However, I got as far as this, which seemed to be enough to answer the required conditions:

OK, now we can look at the questions. Take the chocolate first. We need to have the sneeveling rod turning clockwise, which eliminates D. We also need to have an state where IF the troglodyser is not emitting hydrogen, THEN the queech is also not obulating. All of A, B and C have TH:N, but only switch position C has QO:N. Only position C satisfies all the conditions.

Then second question is a little harder, as there are still two conditions, and the second can be satisfied in one of two ways. Take the first: the rumption mustn't get hot. This narrows it down to B or D. Can B satisfy either of the conditions? We need to see the urfer not curling up AND queech not obulating (nope, both are wrong), OR the pratching valve glowing AND the troglodyser not emitting hydrogen. The pratching valve isn't glowing, so that eliminates B.

Logically, D is the only one left, and so we can be certain that it is the answer (remember Sherlock Holmes?*), but let's look at it to make sure. The pratching valve isn't glowing and the troglodyser is pumping out the old H, so that's no good. However, looking at the alternative, we see that the urfer isn't curling up, and the queech isn't obulating. That satisfies the conditions.

If anyone reading this managed to get a value in all of the grid boxes, please let me know how you did it! I'm sure there must be a way, but it was late when I did this, and sometimes enough is enough, if you know what I mean.

*"It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth."


  1. I thank you! Nice to know the old brain hasn't atrophied altogether...

    That's pretty much exactly how I got the answer, except less tidily as I didn't have to show my working. I couldn't fill the whole grid, either - I don't think it's possible from the information given, even using implied logic for strong probables. For example: whenever PV glows R gets hot does not guarantee the reverse, that R can only be hot when PV glows. It's quite likely, though, so I gridded it too - but anything more with the jolly old urfer would have been pure guesswork!

  2. Ah yes, the 'if it's raining I will wear my coat; I am wearing my coat; therefore it is raining' fallacy. 'Quite likely' doesn't mean 'is'! I didn't permit myself any of those, and I still got there. Some of those 'if X, and either if Y, then Z OR if A then B' are pretty hard to handle without some kind of algebra to nail them down. I did study formal logic once, but it was a long time ago, and not a lot of help to me here.

    But well done: that's three of us who agree, and we are all fine fellows, so we must be right. If I ever get down your way, the first pint's on me.

    Glad your brain is still functioning.

  3. 'Propositional Calculus', that's what it was called. Thursdays, 9.00 am. Hard work for a hung-over student brain.


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