diff --git a/chapter-03/exercises.pl b/chapter-03/exercises.pl
index 1bec336..588be48 100644
--- a/chapter-03/exercises.pl
+++ b/chapter-03/exercises.pl
@@ -31,6 +31,11 @@
 greater_than(succ(_),0).
 greater_than(succ(X),succ(Y)) :-
   greater_than(X,Y).
+  
+%% alternative: 
+greater_than(succ(X), X).
+greater_than(succ(Y), X) :-
+    greater_than(Y, X).
 
 %% Exercise 3.3
 %% Binary trees are trees where all internal nodes have exactly two childres. The
@@ -122,5 +127,12 @@
   directTrain(Z,X),
   travelBetween(Z, Y).
 
+%% alternative: 
+directTrain(X,Y) :- directTrain(Y,X).
+travelBetween(X,Y) :- directTrain(X,Y).
+travelBetween(X,Y) :-
+  directTrain(X,Z),
+  travelBetween(Z,Y).
+
 %% You will end up in infinite loops since you can go both directions, so it is
 %% possible to keep calling the same function over and over.