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PostPosted: Thu Aug 18, 2011 7:05 am 
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Joined: Sat May 28, 2011 2:26 pm
Posts: 10
Would anyone be able help with the following question we have a disagreement in the family regarding the answer :


"Sam the spider is at a corner A of the room. Sam wants to reach the opposite corner B, crawling along the edges of the room and always going further away from A. How many different routes can Sam choose ? "

A diagram of a cuboid is provided where <A> is at the top left-hand corner in front face of the cuboid and <B> is at the bottom right-hand corner on the back-face. (I tried to insert a diagram here but was not successful).

Is there a set method for these sort of questions ?


Any help would greatly appreciated.

Thank you in advance :)


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PostPosted: Thu Aug 18, 2011 7:10 am 
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Joined: Mon Jun 18, 2007 2:32 pm
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Location: East Kent
may well be, but I would probably draw it


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PostPosted: Thu Aug 18, 2011 8:26 am 
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Joined: Wed Aug 01, 2007 11:19 am
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The answer is 6.

My only tip with these sorts of questions is to be systematic, to make sure you don't miss any out or count one twice.

So to start, Sam has 3 choices (as he has to stick to the edges). He picks one of these. Then has two choices, both of which take him further from A so that's ok. He picks one, then has just one choice left that takes him away from A and ends up at B. So for each of the 3 choices he originally has, there are 2 routes. Thus 6 altogether.


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PostPosted: Sun Aug 21, 2011 10:18 am 
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Joined: Tue Aug 16, 2011 2:28 pm
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Location: Hatch End
I agree with aliportico.

The way I would phrase it to my kids would be to ask them to look at the room we are in (hopefully we are in a cuboid of some sort!), and imagine Sam in the corner at point A. Can you see that there are three edges he could travel along? Pick any of those three lines. Can you see that Sam now arrives at a corner, where he has two options (three routes, but one of them is the one he just came from, so that would constitute not going away from point A)? Now travel along either of those two options. At the next corner, Sam only has one option to go down to get to B.

This means that Sam had 3 options at the first corner. For each of those 3 options, he has 2 options at the second corner. He has no further options.

He therefore has 3 x 2 = 6 options in total.


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PostPosted: Tue Aug 23, 2011 8:11 am 
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Joined: Sat May 28, 2011 2:26 pm
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Hello

Thank you so much for helping me out - and agreeing with the answer. :)


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