In Heinlein's Space Cadet, one of many tests administered to the protagonist seems to have no way of scoring any points. See the excerpt below.
Late in the day he was ushered into a cubbyhole containing a chair, a gadget mounted on a desk, pencil and paper, and framed directions.
"If any score from a previous test," Matt read, "appears in the window marked SCORE, return the starting lever to the position marked NEUTRAL to clear the board for your test."
Matt found the window labeled "SCORE"; it had a score showing in it - "37."
Well, he thought, that gives me a mark to shoot at. He decided not to clear the board until he had read the instructions.
"After the test starts," he read, "a score of T will result each time you press the lefthand button except as otherwise provided here below. Press the lefthand button whenever the red light appears provided the green light is not lighted as well except that no button should be pressed when the righthand gate is open unless all lights are out. If the right-hand gate is open and the lefthand gate is closed, no score will result from pressing any button, but the lefthand button must nevertheless be pressed under these circumstances if all other conditions permit a button to be pressed before any score may be made in succeeding phases of the test. To put out the green light, press the righthand button. If the lefthand gate is not closed, no button may be pressed. If the lefthand gate is closed while the red light is lighted, do not press the lefthand button if the green light is out unless the righthand gate is open. To start the test move the starting lever from neutral all the way to the right. The test runs for two minutes from the time you move the starting lever to the right. Study these instructions, then select your own time for commencing the test. You are not permitted to ask questions of the examiner, so be sure that you understand the instructions. Make as high a score as possible."
"Whew!" said Matt.
Still, the test looked simple-one lever, two pushbuttons, two colored lights, two little gates. Once he mastered the instructions, it would be as easy as flying a kite, and a durn sight simpler than flying a copter! - Matt had had his copter license since he was twelve. He got to work.
First, he told himself, there seems to be just two ways to make a score, one with the red light on and one with both lights out and one gate open.
Now for the other instructions - Let's see, if the lefthand gate is not closed - no, if the lefthand gate is closed - he stopped and read them over again.
Some minutes later he had sixteen possible positions of gates and conditions of lights listed. He checked them against the instructions, seeking scoring combinations. When he was through he stared at the result, then checked everything over again.
After rechecking he stared at the paper, whistled tunelessly, and scratched his head. Then he picked up the paper, left the booth, and went to the examiner.
That official looked up. "No questions, please."
"I don't have a question," Matt said. "I want to report something. There's something wrong with that test. Maybe the wrong instructions sheet was put in there. In any case, there is no possible way to make a score under the instructions that are in there."
Was Matt's conclusion correct?