Quesiti in inglese

Quesiti in inglese delle Olimpiadi del Problem Solving

John wishes to walk from corner A to corner B through streets as in the following street map. A route from A to B is a combination only of northward segments and eastward segments; an example is shown in bold on the map ([N,E,E,N,N,N,E,E]).

Note that at any corner John has only two choices; actually he can neither go backward, nor increase the distance from destination.

How many routes are there from A to B available to John?

Let be the set of natural numbers whose digits, in decimal representation, are chosen from {1,2,3} such that no digit is repeated.

Find the sum of all these numbers and put it in the box below.
Hint: note that, for example, the numbers 1, 12, 123 belong to.

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