Solve the following cryptarithmetic problem using Prolog:

P I N G
P O N G
+ F U N
---------
I G N I P

Each of the 7 different letters stands for a different digit. The aim is to find a substitution of digits for the letters such that the resulting sum is arithmetically correct. Your program should find ALL answers, that do not have leading zeros.

It should be possible to query your solution in this manner:

?- crypt(P,I,N,G,O,F,U).

Your solution should then produce all of the combinations of the digits that satisfy the addition problem above. Don't get
confused between the letter "O" and the number "0" (zero).

HINT - use generate-and-test.

HINT - make sure you never let P=N, or G=F, etc... all of the
distinct letters have to stand for distinct digits.

2. Assume that you have a set of facts about airline flights in the following format:
flight(Number,Source,Dest,Leaves,Arrives).
for example:
flight(22,la,ny,10,15).
means that flight #22 leaves "la" at 10am and arrives
in "ny" at 3pm (assume a 24-hr clock, integers only).

Write the following rules:

-- long(Number,Time)
is true for flights which are in the air longer than Time.
-- route(Source,Dest)
is true for each pair of cities for which there is some sequence of flights starting at Source and ending at Dest.
(it doesn't have to display the route, just be true if there is a route).

You may assume that all flights are completed within the 0-24 time period.... that is, you DON'T have to worry about flights
which arrive after the clock "wraps around" back to zero.
The best solutions are queryable.