The Ultimate Guide to Counterintuitive Puzzles

Critical thinking skills can boost your quality of life and ensure that you make the best possible decisions. Since people make about 35,000 conscious decisions on a daily basis, it's important that you flex your brain often and learn how to make the right choices.

Counterintuitive puzzles can help you better understand probability, get mental exercise, and make you more confident in day-to-day decisions. Read on to learn the basics of these types of puzzles and how you can start to play awesome brain games.

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What Are Counterintuitive Puzzles?

In the most basic terms, counterintuitive puzzles are puzzles that go against common thought process to solve. They're mathematical or logical paradoxes.

These puzzles are as challenging and fun as they can be frustrating. Surprisingly, they can decrease stress levels in the long term as well. Completing them gives you a feeling of accomplishment and distracts you from other negativity in your life.

They also give us insight into the ways that our minds work. They exercise our brains, build critical thinking skills, and overall boost cognitive function.

The Monty Hall Problem

The most famous and easily-understandable counterintuitive puzzle is called the "Monty Hall Problem." It's based on the game show Let's Make a Deal. Monty Hall was the host.

In this puzzle, you imagine that you are on a game show. You are placed before 3 doors and get to keep what is behind the one you choose. Behind 2 doors are goats; behind 1 door is a car.

Of course, you are hoping for the car. You pick one of the 3 doors randomly. We'll call it Door A. Behind Door A is the prize that you have tentatively chosen for yourself.

At this point, there is a 1/3 probability that Door A contains the car. Probability is the likelihood of an event. Since you're unsure of what is behind your door, it's important to consider the probabilities of different outcomes.

The game show host then opens one of the 2 remaining doors that you did not choose. We'll call that one Door B. Behind Door B is a goat.

Now you need to choose between your current Door A and the remaining door, Door C. One has the second goat behind it while the other contains the coveted car.

Logically, you would likely think that there is a 50/50 chance that your Door A contains the car. However, this is surprisingly untrue. This is why these types of puzzles are counterintuitive.

Considering probability and statistics is the best way to win the car.

Which Door Should You Stick With?

If you play the game 100 times and always hold onto Door A. This "pick-and-hold" strategy would only win you the car about 33% of the time.

However, let's say that you reset the game and switch to Door C for 100 games. You will only win about 66% of those games.

What gives?

If you keep to Door A no matter what happens, there is no way for you to improve your chances. The host could add a million more doors or decimate all the others with huge hammers. The contents of Door A would remain the same.

So, the best that you can do with Door A is the one in three chance that you initially had of winning. The other door contains the rest of the chances, which is two in three.

Deal or No Deal

To better understand this, you can also think about this in terms of the game show Deal or No Deal. In this program, the contestant (you) must choose one of 26 numbered briefcases at the beginning of your round.

One of these briefcases contains $1 million. The others contain cash amounts from 1 cent; to $750,000.

Your goal is obviously to win $1 million despite the fact that the other cash values are nothing to scoff at either. For the purposes of this thought experiment, let's pretend that all of the suitcases sans the million-dollar case contain 1 cent;.

Let's also assume that you chose Suitcase #1 for simplicity's sake.

Throughout the course of the game, you will choose to eliminate suitcases from the remaining 25. If 1 cent; suitcases are eliminated every time and you (wisely) choose not to make any deals, you will find yourself with 2 suitcases in the final round. One contains $1 million; the other contains one penny.

What Should You Do?

Sticking with Suitcase #1 affords you the original 1/26 chance of winning. The other suitcase (we'll call it Suitcase #26) was filtered from 25 other suitcases.

To put the idea of "filtering" into perspective, the host has taken a set of 25 choices and improved those odds over time. By removing 24/25 of those 1¢ suitcases, he has left the best door of those 25 left for you to pick.

You aren't choosing between two doors that have an equal probability of holding $1 million. Your initial Suitcase #1 is a random selection out of 26. Suitcase #26 is the best of 25 random chances. It's curated, which makes it better.

Shouldn't 2 Suitcases Mean a 50/50 Chance?

The answer to this question is a resounding "no."

This is, of course, counterintuitive! After all, we all learned about coin flips in first grade. You always have a 50/50 chance of winning those regardless of past outcomes... right?

Well, yes. However, our situation is not akin to that of a random coin flip. While you do have 2 remaining options, one of them is heavily curated.

Getting over this preconceived notion is the most challenging part of these hard puzzles.

However, you can replace it with another logical thought: the more information you have, the better your decision will be.

The host of the Monty Hall Problem isn't trying to improve the prize behind your door. He can't wave a magic wand and turn a goat into a Ferrari. You also couldn't do this with a Deal or No Deal suitcase no matter how much you might want to.

What you're holding onto goes completely unexamined and unchanged. It always remains 1/3 or 1/26 or whatever the initial probability was.

The worse possibilities are simply being weeded out of the general pool that may contain the jackpot prize. In the end, your chances will be 2/3 or, in the case of Deal or No Deal, a whopping 24/26.

So... your chances of winning the jackpot are higher if you switch your prize out for the remaining filtered one. That's math; that never changes.

More Awesome Counterintuitive Puzzles

Let's try a couple of simple counterintuitive puzzles. The solutions will be in the section below this one, so do not look at them until you're done!

  1. An apple and a bag of chips cost $1.10 in total. The apple costs $1 more than the potato chips. How much are the chips?
  2. A child had 5 goldfish and all but 4 died, how many fish remain?
  3. Anna's parents have 3 daughters. The first two are named May and June. What is the 3rd daughter's name?
  4. You have 100 pounds of potatoes. By weight, they are 99% water. You dehydrate them until they are only 98% water. How much do they weigh now?

Remember to think critically about these questions before writing down any answers!


Here are the solutions:

  • The chips are worth 5 cent;

Intuitively, you likely wanted to respond that the chips were 10 cent;. However, if the chips cost 5 cent; and the apple costs $1 more, the apple would cost $1.05. $1.05 + 5 cent; = $1.10 in total... the correct answer.

  • 4 goldfish are still alive

Your first guess would likely be 1 goldfish, but the question itself is a trick. It tells you that 4 of the fish are alive since "all but 4 died." Only 1/5 fish died.

  • The daughter's name is Anna

Once again, the question itself gives you the answer. Rather than being July, the logical next name after May and June, the third daughter is Anna herself. May, June, and Anna are the 3 sisters' names.

  • 50 pounds

You probably don't think that reducing the water content would drop the potato weight by that much since the content was only 1% lower.

However, 100 pounds of potatoes means 99 pounds of water (and only 1 pound of solids). You remove 50 pounds of water and are left with 50 pounds of potatoes. The shriveled potatoes are 98% (49 lbs) water and 1% (1 lb) solids. This equals 50 pounds.

Where Can You Find More Counterintuitive Puzzles?

Did you have fun with the above puzzles? If so, that's awesome. And there are ways that you can get more.

Downloading a counterintuitive puzzle app to your Smartphone is one of the best ways to get these games. Digital puzzles are extremely accessible. They also will take you through different difficulty levels so that you can best test your brain.

Enigma Pro is one of the best applications for counterintuitive puzzles. It incorporates over 1000 years of puzzles that you can solve. Many involve math and probability as the Monty Hall problem does while others are more like the word games we played above.

You also may enjoy the Math Puzzles app. This is a great place to flex observation skills, logical reasoning that goes against the grain, and outside-the-box critical thinking.

Boost Your Mind With Awesome Brain Games

Counterintuitive puzzles are fun, challenging, and a great way to tease your brain. Now that you know some logical and probability-related puzzles to try, it's time to begin playing the best brain games.

PuzzleSeek offers the best information about puzzles and brain teasers on the web. We're excited to point you to the best possible puzzles of every difficulty level. Contact us to learn more about counterintuitive brain games and where to start puzzling.

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