Two friends were spending their bank holiday on a cycling trip. Stopping for a rest at a village inn, they consulted a route map, which is represented in our illustration in an exceedingly simplified form, for the puzzle is interesting enough without all the original complexities. They started from the town in the top left-hand corner marked $A.$ It will be seen that there are one hundred and twenty such towns, all connected by straight roads. Now they discovered that there are exactly $1,365$ different routes by which they may reach their destination, always traveling either due south or due east. The puzzle is to discover which town is their destination.
Of course, if you find that there are more than $1,365$ different routes to a town it cannot be the right one.
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