“One should not think slightingly of the paradoxical; for the paradox is the source of the thinker’s passion, and the thinker without a paradox is like a lover without feeling: a paltry mediocrity.” – Søren Kierkegaard
Paradoxes appear in all shapes and forms. Some are simple puzzles of reasoning, while others reveal the foundations of entire scientific disciplines. Many can be solved by careful examination of their hidden assumptions—one or more of which may be faulty. Strictly speaking, these shouldn’t be called paradoxes at all, because once a puzzle is solved, it ceases to be paradoxical.
But there’s a more dangerous category: perceived paradoxes designed to mislead. These contain hidden tricks or sleights of hand that intentionally misdirect the listener. Once the deception is exposed, the contradiction vanishes—but only if you know how to look.
The Hidden Picture
Like Gary Allen described in “None Dare Call it Conspiracy”, discovering deception is like finding the “hidden picture” of a donkey, cart, or boy within another image in a children’s magazine. The picture painters of mass media artfully create landscapes that deliberately hide the real picture.
Once you learn to discover the “hidden picture” in the information presented through newspapers, television, and government announcements—once you can see through the camouflage—you’ll see the donkey, cart, and boy who have been there all along.
The Classic Paradox
Take the simple assertion: “This statement is a lie.”
The words appear straightforward enough, but consider their meaning carefully. The logical paradox becomes obvious as you work through the implications: if “This statement is a lie” is telling you it’s a lie, then it must be false—which means it’s not a lie, making it true—which means it really is a lie, creating an infinite loop.
Join our Telegram channel!
Want our newest articles delivered directly every day? Join the channel for effortless updates!
Join Now →The Mathematical Misdirection
More insidious are falsidical paradoxes—statements that begin sensibly but end in ridiculous outcomes. The absurd result is bogus because of some subtly misleading step in the proof. Mathematical tricks that “prove” 2 = 1 usually involve dividing by zero—something mathematicians know to avoid.
But what about this puzzle?
The youngster at the reception desk charges them €30 for a room with 3 beds in it. They accept to cut the cost of the room equally, every one of them giving €10. They take the key and head up to the room to settle in.
After a couple of minutes the receptionist realizes he has made a fault. The hotel has a special offer on all week and he should only have charged them €25 for the room. In order not to get into trouble with his supervisor, he rapidly takes a bill of €5 from the till and rushes up to correct his mistake. Toward the room he realizes that he simply cannot split the €5 equally between the three men, therefore he chooses to give each of them one Euro and keep €2 for himself. Doing this, he argues, everybody is happy.
Here, then, is the problem we are left with: every one of the three buddies may have contributed €9 toward the room. That makes €27 that the hotel has made, and the receptionist has a further €2, which makes €29.
What has happened to the last Euro out of the original €30?
You may well be able to see the solution to this immediately; I definitely didn’t when I first heard it. Think about it a little before you read the explanation below.
👆 CLICK HERE FOR THE EXPLANATION
This puzzle only seems paradoxical due to the deceiving method it is stated.
The error in the reasoning is that the story added the €27 to the €2 taken by the receptionist, and there is absolutely no reason to do that, because there is simply no longer a full €30 that must be accounted for.
The receptionist’s €2 should be subtracted from the €27 paid by the friends, leaving €25, which is the amount in the till.
This is the same technique used in government subsidies and financial “deals”—make you focus on the wrong calculation while hiding the real math.
The Deeper Pattern
The hotel puzzle demonstrates something crucial: the same misdirection techniques work whether we’re talking about €30 or €30 billion. The principle remains identical—focus attention on the wrong calculation while hiding the real mathematics.
This isn’t just an academic exercise. The ability to recognize mathematical misdirection becomes essential when evaluating government programs, financial products, and media claims that use numerical complexity to obscure simple truths.
Embrace Paradox to Find Truth
Real paradoxes challenge our thinking and reveal hidden assumptions. Fake paradoxes—deliberate misdirection—train us to accept contradictions without question. Learning the difference between the two is perhaps one of the most practical skills in our information-saturated age.
The question isn’t whether you can solve the hotel puzzle. The question is: how many similar tricks do you encounter daily without recognizing the misdirection?
