Math Jam Puzzle / Riddler Express from Tyler Barron

_Math Jam Puzzle or Riddler Express from Tyler Barron.

You are given an empty 4-by-4 square and one marker. You can color in the individual squares or leave them untouched. After you color as many or as few squares as you’d like, I will secretly cut out a 2-by-2 piece of it and then show it to you without rotating it. You then have to tell me where it was (e.g., “top middle” or “bottom right,” etc.) in the original 4-by-4 square.
Can you design a square for which you’ll always know where the piece came from?

https://fivethirtyeight.com/features/can-you-construct-the-optimal-tournament/

output

Testing: [False, False, False, False, False, True, False, False, False, True, True, True, False, False, False, True]
+----+
|    |
| X  |
| XXX|
|   X|
+----+
Testing: [False, False, False, False, False, True, False, False, True, False, True, True, False, False, False, True]
+----+
|    |
| X  |
|X XX|
|   X|
+----+
Testing: [False, False, False, False, False, True, False, False, True, False, True, True, False, False, True, False]
+----+
|    |
| X  |
|X XX|
|  X |
+----+
Testing: [False, False, False, False, True, False, False, True, False, True, True, False, False, True, False, False]
+----+
|    |
|X  X|
| XX |
| X  |
+----+
Testing: [False, False, False, False, True, False, True, True, False, True, False, False, False, True, False, False]
+----+
|    |
|X XX|
| X  |
| X  |
+----+
Testing: [False, True, False, False, True, False, False, True, False, True, False, False, False, True, False, False]
+----+
| X  |
|X  X|
| X  |
| X  |
+----+
Testing: [False, True, False, False, True, False, False, True, True, True, False, False, False, True, False, False]
+----+
| X  |
|X  X|
|XX  |
| X  |
+----+
Testing: [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False]
Testing: [False, False, False, False, False, True, False, False, False, True, True, True, False, False, False, True]
+----+
|    |
| X  |
| XXX|
|   X|
+----+
Testing: [False, False, False, False, False, True, False, False, False, True, True, True, False, False, False, False]
Testing: [False, False, False, False, False, True, False, False, False, True, True, False, False, False, False, True]
Testing: [False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True]
Testing: [False, False, False, False, False, True, False, False, False, False, True, True, False, False, False, True]
Testing: [False, False, False, False, False, False, False, False, False, True, True, True, False, False, False, True]
Testing: [False, False, False, False, False, False, False, False, False, False, False, True, True, True, True, True]
Testing: [False, False, False, False, False, False, True, False, False, True, True, True, False, False, False, True]
Testing: [False, False, False, False, False, False, False, True, False, True, True, True, False, False, False, True]
Testing: [False, False, False, False, False, False, False, False, True, True, True, True, False, False, False, True]
Testing: [False, False, False, False, False, False, True, False, False, False, True, True, True, False, False, True]
Testing: [False, False, False, False, False, False, False, False, False, True, True, True, True, False, False, True]
Testing: [False, False, False, False, False, True, False, False, False, False, True, True, True, False, False, True]
Testing: [False, False, False, False, False, True, False, False, False, True, False, True, True, False, False, True]
Testing: [False, False, False, False, False, True, False, False, False, True, True, False, True, False, False, True]
Testing: [False, False, False, False, False, False, False, False, False, True, True, True, False, True, False, True]
Testing: [False, False, False, False, False, True, False, False, False, False, True, True, False, True, False, True]
Testing: [False, False, False, False, False, True, False, False, False, True, False, True, False, True, False, True]
Testing: [False, False, False, False, False, True, False, False, False, True, True, False, False, True, False, True]
Testing: [False, False, False, False, False, False, False, False, False, True, True, True, False, False, True, True]
Testing: [False, False, False, False, False, True, False, False, False, False, True, True, False, False, True, True]
Testing: [False, False, False, False, False, True, False, False, False, True, False, True, False, False, True, True]
Testing: [False, False, False, False, False, True, False, False, False, True, True, False, False, False, True, True]
Testing: [False, False, False, False, False, False, False, False, False, False, True, True, False, False, False, True]
Testing: [False, False, False, False, False, False, False, False, False, True, False, True, False, False, False, True]
Testing: [False, False, False, False, False, False, False, False, False, True, True, False, False, False, False, True]
Testing: [False, False, False, False, False, False, False, False, False, True, True, True, False, False, False, False]
Testing: [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, True]
Testing: [False, False, False, False, False, True, False, False, False, False, True, False, False, False, False, True]
Testing: [False, False, False, False, False, True, False, False, False, False, True, True, False, False, False, False]
Testing: [False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True]
Testing: [False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False]
Testing: [False, False, False, False, False, True, False, False, False, True, True, False, False, False, False, False]
Falsifying example: test_unique(e=[False,
 False,
 False,
 False,
 False,
 True,
 False,
 False,
 False,
 True,
 True,
 True,
 False,
 False,
 False,
 True])
Testing: [False, False, False, False, False, True, False, False, False, True, True, True, False, False, False, True]
+----+
|    |
| X  |
| XXX|
|   X|
+----+
Traceback (most recent call last):
  File "test.py", line 39, in <module>
    test_unique()
  File "test.py", line 34, in test_unique
    def test_unique(e):
  File "/usr/lib/python3/dist-packages/hypothesis/core.py", line 918, in wrapped_test
    state.run()
  File "/usr/lib/python3/dist-packages/hypothesis/core.py", line 660, in run
    falsifying_example.__expected_traceback,
  File "/usr/lib/python3/dist-packages/hypothesis/core.py", line 519, in execute
    result = self.test_runner(data, run)
  File "/usr/lib/python3/dist-packages/hypothesis/executors.py", line 58, in default_new_style_executor
    return function(data)
  File "/usr/lib/python3/dist-packages/hypothesis/core.py", line 517, in run
    return test(*args, **kwargs)
  File "test.py", line 34, in test_unique
    def test_unique(e):
  File "/usr/lib/python3/dist-packages/hypothesis/core.py", line 464, in test
    result = self.test(*args, **kwargs)
  File "test.py", line 37, in test_unique
    assert not all_unique_selections(boxes), pretty_print(boxes)
AssertionError: None

test.py

import hypothesis

def pretty_print(boxes):
    st = "+----+\n"
    for r in boxes:
        st = st + "|"
        for c in r:
            st = st + bool_to_x(c)
        st = st + "|\n"
    st = st + "+----+"
    print(st)


def bool_to_x(b):
    if b:
        return "X"
    else:
        return " "


def all_unique_selections(i):
    seen_before = []
    for x in [0,1,2]:
        for y in [0,1,2]:
            selection = f"{i[x][y]}{i[x+1][y]}\n{i[x][y+1]}{i[x+1][y+1]}"
            if selection in seen_before:
                return False
            else:
                seen_before.append(selection)
    return True


@hypothesis.given(e=hypothesis.strategies.lists(elements=hypothesis.strategies.booleans(), min_size=16, max_size=16))
def test_unique(e):
    print(f"Testing: {e}")
    boxes = list(zip(*[iter(e)]*4))
    assert not all_unique_selections(boxes), pretty_print(boxes)

test_unique()