solve by emulate the game

Verifying solution...
Test 1 passed!
Test 2 passed!
Test 3 failed  [Hidden]
Test 4 failed  [Hidden]
Test 5 failed  [Hidden]

extra/distract-the-trainers/solution.py

@@ -0,0 +1,47 @@
+def solution(banana_list):
+    fewest_possible_number = len(banana_list)
+    for pairs in generate_trainer_pairs(list(range(len(banana_list)))):
+        possible_number = len(banana_list)
+        for i, j in pairs:
+            if check_loop(banana_list[i], banana_list[j]):
+                possible_number -= 2
+        if possible_number < fewest_possible_number:
+            fewest_possible_number = possible_number
+    return fewest_possible_number
+
+import copy
+def generate_trainer_pairs(trainer_id_list):
+    if len(trainer_id_list) < 2:
+        yield []
+    else:
+        first_id = trainer_id_list[0]
+        temp_list = copy.deepcopy(trainer_id_list)
+        temp_list.remove(first_id)
+        for second_id in temp_list:
+            tt_list = copy.deepcopy(temp_list)
+            tt_list.remove(second_id)
+            for pairs in generate_trainer_pairs(tt_list):
+                yield [(first_id, second_id)] + pairs
+
+def check_loop(x, y):
+    a, b = x, y
+    memo = []
+    while a != b:
+        if a > b:
+            a, b = a - b, 2*b
+        else:
+            a, b = 2*a, b - a
+        if (a, b) in memo:
+            return True
+        else:
+            memo += [(a, b)]
+    return False
+
+tests = [
+        ([1, 1], 2),
+        ([1, 7, 3, 21, 13, 19], 0),
+        ]
+
+for i, o in tests:
+    result = solution(i)
+    print(i, result == o, result, o)