Which way to turn?

james bond didn't even know the day of the week


disoriented from his incarceration, he struggled to the jetty - his mind cleared as he saw the speedboat still there - should he go north or south to escape blofeld's certain pursuit in the faster craft?


safety was closer to the south; and he might not have the fuel for the northern route


blofeld would know all this too, but bond's mind was now clear - he jotted down some figures on a scratchpad and stopped


damn! no watch


his eye caught the transmitter, its battery low


he pressed the button and got the response immediately


"Q here - where the hell are you 007?"


"that's irrelevant Q - just tell me the day of the week"


"monday"


bond heeded the response - monday


he turned north


*** *** ***


why?

Okay, since Mike is being cruel and not posting this response in a hurry ( Id do the same Mike ) I guess I should beg for the answer, however, first Ill have a go at it.


First thing we have to establish is the chance that _I_ can solve this problem, let me elaborate:


Likelyhood that certain knowledge is relevant:


Real Question: (30% chance)


Geography: 8%

Maths: 2%

Bond Movies 10%

Just the info given 10%


Trick/Joke Question: (70% chance)


Bond Movies 10%

US slogans/phrases 20%

Similar jokes 15%

Mikes sense of humour 25%


The % assigned is the chance that the category is the most important factor .. so ... on the Joke side of things Im struggling, I know very little apart from the info given, on the real side of things im not much better off.


Well, we know Bond is disorientated and to me it seems as if too much emphasis is placed on the fact he doesnt know the day, so I will guess that the day is unimportant, Therefore, the only information I consider relevant IF _I_ can solve this (which I dont think I can) is that he heads North.

If the only information is that he heads north, and I can solve the problem on that data, I guess he must be at the South pole.


Despite the fact that this is unlikely given the percentages outlined above, I believe it is the only logical conclusion i can draw.


Now tell us dammit :P

lol! a far better answer than mine!



but here goes



this is a fantastic way to calculate correct strategies - i would recommend you keep a note of the method - it will come in useful in all sorts of situations - in fact, for any "game" in which each player has two choices this is the simple recipe to find the best strategies



first, form a table showing the hero's chances of winning, in rows, against the villain's choices, in columns



in this case, we set the following chances that bond will escape:



<PRE> blofeld north blofeld south

bond north 40% 80%

bond south 100% 70% </PRE>



take the numbers in the last column from the numbers in the first column:



40 - 80 = -40

100 - 70 = 30



ignore any minus signs and swap the results round:



30

40



choose the two strategies in proportion to these numbers



here, since 30 + 40 = 70 bond chooses to go north with a probability of 30/70 or 3/7 times, and to go south 4/7 times



as bond has no randomising device handy (say, the second hand of a watch) he mentally assigned sunday, monday, and tuesday to north, and called Q



his chance of escape is maximised at 74% by this strategy = (80 x 3/7) + (70 x 4/7)



as you can check for yourself, blofeld, making the same calculations from his (columnular) point of view, maximises his chance of catching bond by going south with a probability of 6/7

Thanks for that Mike, another great post, hadn't occured to me that he was randomising, even though it (as always with these things) now seems so obvious.

It's a really good puzzle and fair too, I underestimated the likelyhood that it was solvable.

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