Enigma 1465: To the far quarter
5 February 2013
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From New Scientist #2626, 20th October 2007
On a sheet of graph paper marked out in square cells, using its lines I picked out a square area, which I divided into four square quarters.
In considering the number of different ways using only the lines of the graphs paper in which I could take the shortest route from the top left-hand corner of my area to a corner of one or more of the cells, I found the same answer (six) for the corners reached by going down one cell and across five, or by going down five and across one, or by going down two and across two.
I have now found four corners that can all be reached from the top left-hand corner of my area by the same number of different shortest routes using only the lines of the graph paper. All four of these corners are either on the border of or inside the bottom right-hand quarter of my area.
If I tell you that the answer is less than 10,000, tell me how many different shortest routes there are to each of these corners.