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This Python program examines all assignments of names to colleges. It runs in 1.4s.

Solution:It is certain that Westminster College has two men in the team. They are Graham and Jack.There are two possible scenarios:

Each possibility has three men with the same name (three Freds in the first case and three Kens in the second one), and two colleges with two men (Westminster and Unity in the first case, Sanctity and Westminster in the second).

I found this quite an intricate Enigma to code. Some preliminary analysis can identify the colleges attended by the 3 men with the same name:

If K is the triple name, then 1981 implies 3 K’s attend T,U,V

If J is the triple name, then 1982 implies 3 J’s attend 3 of U,V,W,S

1981 implies 2 J’s attend 2 of T,U,V, therefore U,V.

1983 implies 2 J’s attend 2 of V,S,T, therefore V,S

3 J’s must attend U,V,S

If H is the triple name, 1982 implies 3 H’s attend 3 of U,V,W,S

1981 implies 2 H’s attend 2 of T,U,V, therefore U,V

1983 implies 2 H’s attend 2 of S,T,V, therefore S,V

3 H’s attend S,U,V

If F is the triple name, 1983 implies 3 F’s attend S,T,V

If G is the triple name, 1984 implies 3 G’s attend 3 of S,T,U,W

1981 implies 2 G’s attend 2 of T,U,V, therefore T,U

1983 implies 2 G’s attend 2 of V,S,T, therefore S,T

3 G’s must attend S,T,U

So, some code: