@joe-shmo saidSorry, just to clarify. There aren't 4^6 journey end points, there are 4^6 paths, but that is all we need to know for this question...how many paths there are.
"It's not as easy as that"
Actually venda, it is that easy.
You have a 6 letter string
ALL possible ending points are counted by the multiplication principle of possible directions for each step.
S1,S2,S3,S4,S5,S6
4*4*4*4*4*4 = 4^6 possible strings and hence 4^6 journey ending points.
If you are interested, I will pose another question along these lines?
@joe-shmo saidThanks for the puzzle Jo.
Sorry, just to clarify. There aren't 4^6 journey end points, there are 4^6 paths, but that is all we need to know for this question...how many paths there are.
If you are interested, I will pose another question along these lines?
Seems I "overthought" it
I will always look at any puzzle to see if it interests me.
Whether I can solve it or not is another matter but it puts me to sleep at night thinking on it!
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@venda saidYou had 90% of the work done. Not seeing that last 10% was just a normal case of not seeing the forest through the trees! Good Work!
Thanks for the puzzle Jo.
Seems I "overthought" it
I will always look at any puzzle to see if it interests me.
Whether I can solve it or not is another matter but it puts me to sleep at night thinking on it!
@joe-shmo saidEither I have misread the question,or the answer is none!
Ok...same thing, more steps.
Starting at "P": In exactly 11 steps , how many ways can you get to a location 3 units North and 1 unit East of "P"?
You can reach a location 3 steps north and 1 step east of P in 4 steps.
Therefore,you need to take 7 steps to walk from P to P or an equivalent position.
This is the same as the much publicised "bridge" problem of old.
It can't be done!
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@venda saidCorrect! Well done.
Either I have misread the question,or the answer is none!
You can reach a location 3 steps north and 1 step east of P in 4 steps.
Therefore,you need to take 7 steps to walk from P to P or an equivalent position.
This is the same as the much publicised "bridge" problem of old.
It can't be done!
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@venda saidAfraid not. If you haven't yet; start with k = 1 step and work your way up. The pattern should jump out at you within the first few "k". Proving it in general for all "k" isn't quite so simple.
3K?
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I've tried all that,with little dots on a piece of paper.
First, I went up to 7 "dots" in a straight line east and put a dot at north and south at every step.
I then added up the dots and came up with the answer 3k+1(1 representing an 8th step east)
I then tried with random directions (e.g 2 steps east 1 step north etc) but could only count 3k this way.
I suspect I need a different approach or a bigger piece of paper!!