When it’s time for students to learn mathematics in school, it can be difficult for them to understand how they’d ever apply it in “real” life. Sure, there are some aspects of calculus that we’ll never use when, say, preparing our taxes, but they’re still important to know… right?

Well, if you paid enough attention in math class instead of playing games on your TI-83+, then you just might be able to crack these seemingly impossible equations and puzzles. But be warned: countless people have attempted to conquer them, but only a few have figured it out!

Can you solve the unsolvable? Upon first glance, this numerical nonsense may look like something you learned in second grade, but you won’t be able to solve it using traditional arithmetic…

1-impossible-math-equationhttp://junkhost.com
Are you stumped? You aren’t the only one! This challenge wouldn’t be nearly as interesting if the solution to it was straightforward. Luckily, there are two ways to solve this puzzle…

The first way to pinpoint the answer to this unusual question is to study all the numbers on the left side of the equation. What do they have in common, and how does that relate to the numbers on the right side?

It’s actually quite a bit less complicated to work out the solution to this problem than it may initially appear if you’re paying attention. For example, one plus five equals six, not 18. But six multiplied by three is 18. Could we have discovered the hidden code?

If you apply that same logic to the next set of numbers, you’ll notice it follows the sequence. Two plus 10 is 12, and if you multiply that by three as you did with the set of numbers above, you get 36. The same goes for three plus 15. So, what would four plus twenty, multiplied by three become?

The answer to the question mark is 72, of course! There’s one other method: if you look at the “answers” of each individual equation, you’ll notice that the scalar factor of the number nine gets raised by two each time: nine times two is 18, nine times four is 36, nine times six is 54. Therefore, nine times eight is 72!

5-impossible-math-equationhttp://giphy.com

Need a break from math, but still want to solve a puzzle? Try this riddle: as summer drew to a close, Prince Charming went out in search of his true love and came across a witch’s shack. The prince, exhausted by his quest, asked if he could stay with the witch for the night.

She obliged, but the following morning she presented him with a gift. “One day,” she predicted, “you will find your passage blocked by a wide river without a bridge to pass over it. Your only choice will be to swim to the other side. Fortunately, you’ll never be let down by this magic tunic!”

After thanking the witch, Prince Charming continued his journey, and 100 days later, he located the river that she’d told him about. Amazingly, however, he didn’t need the magical tunic to cross the river! Why do you think that was?

Remember: when Prince Charming met the witch, summer was almost over—meaning it was September. By the time 100 days had passed and he reached the river, the cold would have turned the water into ice, making it easy for him to simply walk to the other side!

For a different type of challenge, try this one: four men face the same direction while standing on descending steps, one in front of the other. However, a fourth man is separated from the group by a wall. He stands on the other side of it.

The first man can see the second and third men directly in front of him; the second man can only see the third man standing in front of him, and the third and fourth men can see no one.

Meanwhile, none of the men know what color hats they’re wearing on their own heads. All they know is that, among the four of them, there are two white hats and two black hats. They are instructed to shout out their hat colors once they’ve figured out which color it is.

The men can’t move or turn at all, they can’t talk, and their hats must stay on their heads. And, of course, the wall is separating the first three men from the fourth. With that in mind, you must answer: if they all follow the instructions, which one would be the first to shout by process of elimination, and why?

It’s the second man! He can confidently speak up because the third and fourth men can’t see the others, while the first man must know his hat is either black or white because he sees both colors on the men in front of him. So how would the second man know?

The second man knew because he only saw a black hat. Since he knew Man 1 behind him could see two hats, he should’ve shouted out his own hat’s color if Man 2 was also wearing black. But since Man 1 was silent, Man 2 could assume he wore a white hat. Hats off to you if you answered this correctly!

U.S National Archives / Wikimedia Commons

Here’s one last puzzle for you to exercise your brain: a man was changing his tire when all four of his lug nuts fell into a sewer grate. He had no way to retrieve them, and he wondered how long he’d have to wait on the street.

Fortunately, a girl riding by on her bicycle had a clever solution, and the driver had a way to put a new tire in and safely make his way to the closest gas station. What do you think the child explained to him?

The girl on her bike instructed the worried driver to temporarily take just one lug nut from all of the other tires on the vehicle, and use all of those to secure the replacement tire on the car.

From there, the man could drive reasonably safely for the time being until he could get it properly repaired. At that point in time, every tire had three lug nuts, which would be enough to keep the fourth tire in place!