The hardest viral math problems of the year
The internet seems to have a love-hate relationship with math.
People couldn’t get enough of math questions this year as they debated the answers in Twitter threads and parenting forums. But they also lamented how much the complicated problems made their brains hurt.
Here are 11 math problems, brainteasers, and SAT questions that went viral this year.
Only 2% of people were able to figure out this riddle in less than 60 seconds.
Adam Spencer, a comedian, a mathematician, and the author of “The Number Games,” created a riddle that only 2% of people could solve within one minute, according to Reader’s Digest.
He wrote down the numbers one through 19 out of numerical order:
8, 18, 11, 15, 5, 4, 14, 9, 19, 1, 7, 17, 6, 16, ?, ?, ?, ?, ?
To solve the riddle, you need to figure out how he ordered the first 14 numbers and finish the riddle by adding the last five.
The five missing numbers are two, three, 10, 12, and 13. The pattern is that the existing numbers are listed in alphabetical order.
The completed set of numbers looks like this:
8, 18, 11, 15, 5, 4, 14, 9, 19, 1, 7, 17, 6, 16, 10, 13, 3, 12, 2
A math question for fifth graders in the Chinese district of Shunqing stumped adults around the world.
The problem translates to: “If a ship had 26 sheep and 10 goats onboard, how old is the ship’s captain?”
How is the amount of cargo a ship contains supposed to help you figure out how old the captain is?
The internet had a lot to say about this seemingly impossible math question, which became a trending topic on Twitter.
After the test question went viral, the Shunqing Education Department released a statement saying that the question was meant to gauge “critical awareness and an ability to think independently,” according to a BBC translation.
The question is: “There are 49 dogs signed up to compete in the dog show. There are 36 more small dogs than large dogs signed up to compete. How many small dogs are signed up to compete?”
Popular reasoning was that if there are 49 dogs total, and there are 36 more small dogs than large dogs, you’d subtract 36 from 49. By that measure, there are 13 large dogs and 36 small dogs, meaning the answer is 36. But seeing as that would mean there are 23 more small dogs than large dogs, that isn’t right.
The teacher who gave the question later told Popsugar, “The district worded it wrong.” But as it stands, the answer is 42.5: 49 – 36 = 13, 13 / 2 = 6.5, and 36 + 6.5 = 42.5. Apparently, half of a dog competed at the dog show.
Mumsnet user PeerieBreeks shared the riddle on the parenting site, where it racked up nearly 500 comments with other users debating the answer.
Here’s the question: “A man buys a horse for $60. He sells the horse for $70. He then buys the horse back for $80. And he sells the horse again for $90. In the end, how much money did the man make or lose? Or did he break even?”
Answers in the Mumsnet thread ranged from making $10, $20, and $30 to breaking even. So what’s the solution?
What seems to be throwing people off is the fact that the man sells the horse for $70 and then buys it back for $80, making it look like he spent $10 more. But the correct way to solve the problem is to think of the two transactions as separate: -60 + 70 = 10 and -80 + 90 = 10.
The man makes $10 with each sale, therefore he earns a total of $20.
Author Ed Southall shared a math problem on Twitter that some people managed to get right.
Ed Southall, author of “Geometry Snacks,” shared a photo of a pink triangle inside a square and challenged people to figure out how much of the square is shaded pink. Some Twitter users gave up immediately, but others rose to the challenge.
According to Business Insider’s quant reporter, Andy Kiersz, the key to solving the problem is the height of the pink triangle.
The area of a triangle is 1/2 (base x height). If we assume that the square is a 1 x 1 unit, we can see that the base of the pink triangle is 1, the length of the square. All we need to figure out is the height.
“The key trick is that the little triangle up top is similar to the pink triangle, which means that the little triangle is just a smaller version of the pink triangle,” Kiersz said.
“A property of similar triangles is that the ratio of the triangles’ heights will be the same as the ratio of their bases,” he said. “Since the pink triangle’s base is twice the little triangle’s base, its height is also twice the little triangle’s height. But we know that the little triangle’s height plus the pink triangle’s height is 1, so that means the pink triangle’s height is 2/3. Plug that on in and we get our area = 1/2 x base x height = 1/2 x 1 x 2/3 = 1/3.”
Southall confirmed that the answer is indeed 1/3.
A math problem meant for 8-year-olds went viral after parents couldn’t solve it.
Mumsnet user lucysmam turned to the internet for help with her daughter’s math assignment.
The problem reads as follows:
“On the coast there are three lighthouses.
The first light shines for 3 seconds, then is off for 3 seconds.
The second light shines for 4 seconds, then is off for 4 seconds.
The third light shines for 5 seconds, then is off for 5 seconds.
All three lights have just come on together.
1) When is the first time all three lights will be off at the same time?
2) When is the next time all three lights will come on together at the same moment?”
Thankfully, YouTube math whiz Presh Talwalkar offered an explanationon his channel, MindYourDecisions.
According to Talwalkar, the easiest way to answer the first question about when the lights will all be off is to map out the intervals for each lighthouse and see where their “off” sections overlap. The answer: after five seconds, when the third light has just turned off and the first and second lights are still off.
To determine when all of the lights will come on together, you need to find the smallest common multiple of the intervals when the lights will be on. The answer to that question is that the lighthouses will all come on together at 120 seconds, or two minutes.
For a more detailed explanation, click here.
A tricky math problem created by Gergely Dudás used ice cream cones instead of variables.
Artist Gergely Dudás, who is known for his tricky hidden-object puzzles, shared a math problem on his Facebook page that he illustrated with ice cream cones.
The brainteaser consists of four math equations, each of which adds to or multiplies a numerical sum or product. In place of variables like x or y, however, the brainteaser substitutes ice cream cones that are either empty or have scoops of white ice cream, pink ice cream, or both.
To solve the puzzle, you have to figure out what number the empty ice cream cones, white ice cream scoops, and pink ice cream scoops each represent.
The answer is that the empty ice cream cone represents the number three, the white ice cream scoop represents the number two, and the pink ice cream scoop represents the number one.
A Quora thread of difficult SAT math questions included one people called the “meanest test problem ever.”
“In a class of p students, the average (arithmetic mean) of the test scores is 70.
In another class of n students, the average of the scores for the same test is 92.
When the scores of the two classes are combined, the average of the test scores is 86.
What is the value of p/n?”
Talwalkar shared a step-by-step solution to the tough problem in a YouTube video.
There are a few ways to solve it, but Talwalkar presented a simple shortcut.
The first class had an average of 70. That’s 16 points below the average score of 86. In other words, 86 – 70 = 16. Since there are p students in the class, the difference from the average is 16 p.
The second class had an average of 92. That’s 6 points more than the average of 86. In other words, 92 – 86 = 6. There are n students in this class, so the difference from the average is 6 n.
Because these classes average out together — as the problem says, “when the scores of the two classes are combined” — the deficit of points has to be equal to the surplus of points. Therefore, 16 p is equal to 6 n.
Turning that into an equation, we can easily figure out what p/n is:
16 p = 6 n
p/n = 6/16, or 3/8.
The Riemann hypothesis was first posited by Bernhard Riemann in 1859. It states that the distribution of prime numbers might follow a pattern described by an equation called the Riemann zeta function. To solve the hypothesis, you need to find a way to predict the occurrence of every prime number, even though primes have historically been regarded as randomly distributed.
The $1 million prize goes to whoever can prove that the equation applies to all prime numbers. British mathematician Sir Michael Atiyah said he solved the 160-year-old problem, but his solution needs to be peer reviewed before he can take home the prize money.
Similar to Sudoku, this puzzle created by Puzzles9 consists of a rectangle with nine squares, each containing a number, except for the bottom-right square.
Read the first two rows of numbers horizontally, each as one number — 289 and 324.
The pattern is that 17 x 17 = 289 and 18 x 18 = 324. So it stands to reason that the bottom row will be 19 x 19 = 361. Therefore, the missing number is one.
This brainteaser features three pentagons, each with a set of five numbers.
This brainteaser created by Puzzles9 presents three pentagons, each with a set of five numbers. The middle pentagon is missing a number in the bottom-right corner.
From left to right, let’s label the pentagons A, B, and C. The difference between the numbers in pentagons A and B can be found in Pentagon C in the same location across the board. In other words, Pentagon B – Pentagon A = Pentagon C.
So, the missing number is 10.