... back to the drawing board
If your calcs are correct, P can't be on the far right of the grid so the useable grid will be narrower than 10 blocks. Run it again with a narrower grid values.
If your calcs are correct, P can't be on the far right of the grid so the useable grid will be narrower than 10 blocks. Run it again with a narrower grid values.
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I assumed GCS at top left corner of grid, and although the grid is # blocks wide, there are #+1 vertical paths.
The workplace can't be at east 3 or east 4. You can't travel West so all the paths above and to the East of P are eliminated.
Why assume it? It's stated in the OP.
Clearly.
And yet, it is.
It appears that you're trying to find a route from P to GCS, whereas the question clearly asks for a route to work, i.e. from GCS to P.
Hi Softus.
Completely agree with your first two points, disagree with the third, and although my first stab at an answer was pants I assure you I'm not trying to find a route from P to GCS.
Completely agree with your first two points, disagree with the third, and although my first stab at an answer was pants I assure you I'm not trying to find a route from P to GCS.
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Greetings blondini.
Reading my third point again, I disagree with it too.
Unless you're referring to this:
...in which case I disagree with you.
S
Shutpa
Softus, have never tried this before but hopefully the grid will appear, albeit on its side. If it works, you will see the actual grid from the paper! View media item 8337
View media item 8339
W is Gordon's workplace.
W is Gordon's workplace.
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I cannot imagine a child of 12 being expected to find this answer by calculation....
Therefore surely we must be into patterns - hence excel, I guess a sheet of paper would suffice- as Bolo has more or less shown ...
If each grid intersection is numbered by a particular method - think Pascal, then it should be possible for each number to reflect the sum of routes to that spot from the start point... I bet we'd find just one instance of the figure 364, (maybe not at 3,14 ) ... this will be the 'home' point... I think it will be the only point with the value 364 due to the wording of the Q .... "...but that on January 1st 2010, he would need to repeat a route already used..." I see that as confirmation that 364 is the max number of routes he could take. ( IMO Questions for children should not include 'red herrings' I do not beleive this question does. Every part has a meaning. )
Why did I ignore, in my patterned spreadsheet a swathe of cells? Because I know that 3 from 14 has the same result as 11 from 14 ... 11 and 14 are not available together... If you see what I mean... However flawed !
As I said, drawing board.
Therefore surely we must be into patterns - hence excel, I guess a sheet of paper would suffice- as Bolo has more or less shown ...
If each grid intersection is numbered by a particular method - think Pascal, then it should be possible for each number to reflect the sum of routes to that spot from the start point... I bet we'd find just one instance of the figure 364, (maybe not at 3,14 ) ... this will be the 'home' point... I think it will be the only point with the value 364 due to the wording of the Q .... "...but that on January 1st 2010, he would need to repeat a route already used..." I see that as confirmation that 364 is the max number of routes he could take. ( IMO Questions for children should not include 'red herrings' I do not beleive this question does. Every part has a meaning. )
Why did I ignore, in my patterned spreadsheet a swathe of cells? Because I know that 3 from 14 has the same result as 11 from 14 ... 11 and 14 are not available together... If you see what I mean... However flawed !
As I said, drawing board.
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Now to any 'node' the values are correct .. There is more to do, but
The next pattern - not there yet - But I will jump the gun at Gordo's workplace being at 11 blocks South, 3 blocks East.
The block distance to each intersection is shown.
My original did not use full path to intersections in the calcs.
And as always I reckon I'll muddle between Combinations and Permutations !
BTW Softus had it in his pix - well 11,3 is correct I reckon. Blondini was on track too...
The next pattern - not there yet - But I will jump the gun at Gordo's workplace being at 11 blocks South, 3 blocks East.
The block distance to each intersection is shown.
My original did not use full path to intersections in the calcs.
And as always I reckon I'll muddle between Combinations and Permutations !
BTW Softus had it in his pix - well 11,3 is correct I reckon. Blondini was on track too...
Finally had time to work this backwards and with a fresh supply of used envelopes to scribble on I have deduced, (before reading the latest posts), that Softus has indeed excelled.
Now what if Gordon takes a 10 minute stop for a Bagel and latte?
Now what if Gordon takes a 10 minute stop for a Bagel and latte?
S
Shutpa
My hearty congratulations Softus. Bearing in mind that the UK Junior Mathematical Challenge is set by 'The Acturial Profession' and is aimed at those gifted in mathematics, I am truly impressed. You have shown that the comment posted on the original question about the width of the river, was nothing more than jealousy and sour grapes. I speak of course of Namsag's post that claimed that your mathematical abilities couldn't even match those of a twelve year old. Do I hear a whispered apology from Namsag?
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