Whether you read the question wrong, forgot to use PEMDAS, or overlooked something little, math problems can be extremely deceptive. That’s partly the reason why simple math problems go viral all the time, they seem incredibly easy, but people always get vastly different answers and into intense arguments over it. While most of the math problems seem impossible to solve, sometimes all you really need to do is use some logic.
So, without much further ado, here are 15 simple math problems that most people cannot solve.
15. The Bat & The Ball
This is a classic problem that has stumped almost everyone who has come across it.
The question is: “a bat and ball cost one dollar and ten cents. The bat costs one dollar more than the ball. How much does the ball cost?”
We’ll give you a second to think about it. Ok, got your answer? Did you say ten cents? If so, you’d be wrong. The answer is that the ball costs five cents. When you first read the problem and hear that the bat is a dollar more than the ball, and the bat and the ball cost a dollar and ten cents, your brain assumes that the ball is automatically 10 cents. However, if you do the math, you see that the difference between a $1 and 10 cents is actually 90 cents, not $1. The only way for the bat to be a dollar more than the ball is if the bat is $1.05 and the ball is 5 cents.
14. The Lily Pad
There is a patch of lily pads on a lake. “Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?”
You’re probably thinking the answer must be 24, but you’d be very wrong. The answer is, it would take 47 days for the patch to cover half of the lake. When you hear “to cover half of the lake”, your brain thinks that all you have to do is divide 48 by 2, which would be half, or 24. However, that’s the wrong logic. If it takes 48 days to cover the entire lake, and it doubles in size everyday, then the day before would be half of the fully covered lake. Therefore, the answer is on the 47th day. Here, we’ll give you some time to try it out again.
Chances are you have probably seen this question floating around Facebook. This question has caused a great divide, as some people believe the answer is 1, while others are certain the answer is 9. The answer is, drum roll please…9!
Remember PEMDAS? The order goes Parentheses, Exponents, Multiplication Division, Addition and Subtraction. The reason this simple equation has people confused is because of the way people interpret PEMDAS. Just because a number touches a parentheses, 2(1+2), does not mean that it should be multiplied before the division, 6÷2(1+2), to the left of it. According to PEMDAS, you have to solve for what is inside the parentheses, then exponents, then multiplication, then division, but most importantly, “from left to right in the order both operations appear.” As a result, after you solve everything inside of the parentheses, and floating from left to right. Therefore, 6÷2(1+2) = 6÷2x(1+2) = 6÷2×3 = 3×3 = 9.
12. The Monty Hall Problem
Let’s pretend you’re on a game show. The host gives you a choice of three doors to choose from. Behind one door is a brand new car, and behind the other two doors is nothing. Lets say you pick door number one, and since the host knows which door the car is behind, decides to open another door. The host opens door number two, and shows that there is nothing behind it. But then, the host gives you a new option; you can stick with your original choice or switch doors. The question is, do you stick with your original choice or change your mind?
While you may think that you have a 50/50 chance of winning the car because there are only two doors left, you’d be sadly mistaken. You should always switch. You initially had a 1 in 3 chance of picking the prize winning door, which means you had a 2 in 3 chance of picking a door with nothing behind it. So when the host reveals an empty door and eliminates a wrong choice, the chances that the car is behind the last door is 2/3, which is twice as great as the odds were that you picked the right door on your first try. By switching, you are betting on the 2 in 3 chance you picked the wrong door on your first try. Let’s try to remember this next time you’re on a gameshow.
11. Number Puzzle
This type of number puzzle is meant to improve your logical thinking. There are also specific rules for these types of number puzzles. You first have to figure out the pattern that the puzzle follows, and then you have to answer the puzzle according to the established pattern. With all of that being said, looking at the picture, can you figure out what number the question mark is supposed to be? Did you guess 6? If so, you would be right! According to the pattern of the puzzle, the numbers in each row and each column add up to 15.
10. Fast Addition
For this next problem, don’t use a calculator or paper to try to solve it. What do you get when you add 1,000 + 40 + 1,000 + 30 + 1,000 + 20 + 1,000 + 10? Did you also get 5,000? Sorry to say, but that is wrong. The correct answer is 4,100. If you got it wrong, don’t feel bad a lot of us do. Your brain was just getting ahead of itself! You were probably doing great up until the last number. 1,000 + 40 + 1,000 + 30 + 1,000 + 20 + 1,000 = 4,090. 4,090 + 10 = 4100, not 5000. Rats! The thing is, that when you were adding everything up, you didn’t get use to carrying any of the ones over, and when you finally got to the last number, you accidentally added it to the thousands spot rather than the hundreds spot because you were going so.
9. Three Line Equation
For this next one, all you have to do is find the answer to the equation. The answer to this equation is actually 2. Did you make the mistake of multiplying 1 x 0 first, and then adding up the rest of the ones in every row to get 12? Sorry, that wasn’t the correct way of solving this. The reasoning behind this is because there are no operator symbols, such as plus or minus, at the end of each line. So there is no reason to assume that each of the lines are part of the same equation. Math is simple logic and you can’t assume things that aren’t stated. Which can make it hard at times for us. Furthermore, since there are no equal signs at the end of the first two lines, they are not equations, but instead-expressions. As a result, the only real equation is the last line. 1 + 1 x 0 + 1 = 2. Boom!
8. 0.999… is 1?
This next problem is a true or false question (finally).
True or false: 0.999… = 1.
False, right? Well…actually the correct answer is true. How is that possible, you’re probably asking? If you put three “…” in a row after a number, that means it goes on indefinitely. So 0.999… can never equal 1, right? Sorry, but 0.999… does equal 1 and we can prove it to you. Here is a pretty simple way of looking at it. We all know that 1/3 = .333… If you multiply both sides by three you’ll see that 3/3 equals 0.999… Therefore, 3/3 = 1 = 0.999… Would you look at that! The reason people have a hard time believing this is because the idea of infinity is a hard idea to grasp. Most people imagine a final 9 somewhere down the line. It’s actually pretty simple when you break it all down.
7. Broken Water Heater
Illustration courtesy of sanfordkramer.com
Let’s say, the water heater in your apartment broke, so you could no longer take a shower. You found someone to help, showed them the broken water heater, they used a bunch of random parts and were able to fix it. You paid them for the repair and went on your way. Is this person more likely “an accountant?” OR “an accountant and a plumber”? Did you say plumber? Wrong. The answer is, this person is most likely an accountant. Since the scenario makes it sound like the person is a plumber, you naturally thought they were a plumber. Nevertheless, anyone who is an “accountant and a plumber” is also an accountant. This is a probability question, so the probabilities are (A) a plumber-accountant fixed your heater and (B) an accountant fixed your heater. Since in this situation, any plumber is also an accountant, so you have to add those probabilities together. Therefore, A ≤ A + B.
6. Parking Spot Number
This next problem went viral over Twitter after people found out this question was given to 6-year-olds in Hong Kong and they were expected to solve it in 20 seconds or less. Now, let’s see what you got-set those timers and…go! Were you able to solve it in time? We’ll give you a small hint. It doesn’t require any math. Still nothing? We’ll give you the answer anyway. It’s 87. You’re probably wondering how you get 87, given that the sequence of numbers is 16, 06, 68, 88, X, 98. Well, to figure this one out, all you have to do is flip the picture upside down. Now you can see that the real order of numbers is 86, X, 88, 89, 90, 91. Guess it wasn’t that hard after all.
5. Problem With Fruit
This fruit-based math problem has been driving people nuts! How much does the coconut, apples, and bananas equal? Everyone seems to think the answer is 16. And they would all be wrong. The correct answer is actually 14. There’s no trickery involved with this one, you probably just counted wrong (sorry). For the first line, it appears that the apple has a value of 10. For the second line, the bananas have a value of 4. Then, on the third line, the coconuts have a value of 2. If you were to plug those values into the final line, you would get 2 + 10 + 4, which equals 16. However, if you look closely, the fruit are slightly different. There is half a coconut, instead of two halves, and there are 3 bananas, instead of 4 from earlier. Therefore, if you reduce the numbers according to the new portions of fruit, you get 1 + 10 + 3, which equals 14.
4. The Missing Dollar
This problem is actually very simple, but it has been haunting our brains trying to figure it out. A kid wanted to buy a $97 shirt. He borrowed $50 from his mom and $50 from his dad. He bought the shirt and had $3 left over. He gave $1 back to his mom and $1 back to his dad (Warning! Here comes the hard part). Now the child owes his mom $49 and his dad $49. $49 + $49 = $98 + the kid’s $1 = $99. Where did the other $1 go? Go ahead and think about it. Still can’t figure it out? Allow us to explain it. The problem is that you are adding the extra $1 to the $98, not subtracting. The original price of the shirt was $97, so $49 + $49 = $98 MINUS the kid’s $1 = $97. There was no missing $1. Mind BLOWN.
3. More PEMDAS
This next problem is very simple and very easy to mess up. Which is why people have such a hard time solving it. Most people start by figuring out the division in the middle, then add 1 to the sum before subtracting it from 9. Therefore, 3 divided 1/3 is 9, plus 1 equals 10. 9 – 10 = -1. The only problem is -1 is incorrect. When you see a 3 and 1/3 sitting next to each, your instinct is to combine them into a 1. Well, we’re here to tell you not to do this because you’ll end up with 9, another common and incorrect solution. How do you solve it though? 3 divided by 1/3 gives you 9. 9 minus 9 is 0. 0 plus 1 is 1. There you have it. Not so hard, huh?
2. People On The Bus
This question was taken from a second grade-equivalent standard assessment test and has been causing countless arguments ever since. The question is a follows: “There were some people on a train. 19 people get off the train at the first stop. 17 people get on the train. Now there are 63 people on the train. How many people were on the train to begin with?”
Some people argue that the answer is 46, others say it’s 2. Some people believe that it’s a trick question. Others ask, “what about the conductor?” The answer is simply 65. All you have to do is work backwards. 17 people get on the train. Now there are 63 people on the train. You have to subtract the 17 people from the 63 people on the train now. 63 – 17 = 46. 19 people get off the train at the first stop. Now, add 19 to the 46 on the train after the first stop. 46 + 19 = 65.
1. Happy Birthday
People have been racking their brains over how to figure out this last problem. While this problem may seem impossible, it’s actually much simpler than you think when you break it down with logic. Let’s go through it step by step, shall we? First, you have to figure out if Albert knows the month or the day. If Albert knows the day, then there’s no way that Bernard knows the birthday, so Albert must know the month. From Albert’s statement, we know that Albert is certain Bernard doesn’t know the birthday, so May and June can be ruled out because day 19 only appears in May and day 18 only appears in June. If Albert had May or June, then he can’t be sure that Bernard doesn’t know, since Bernard could have had 18 or 19. Now, Bernard can know which month it is; it has to be July 16, August 15 or August 17. Now, the only way Albert can be certain of the date, he must know it’s in July. If it was August, Albert couldn’t be sure, as there is August 15 and August 17. As a result, the answer has to be July 16. See, that wasn’t so hard.