A math problem can often look super simple... before you sit down to actually do it and find you have no clue how to solve it. Then there are the problems that make you feel like a math whiz when you solve it in 2 seconds flat — only to find your answer is WAAAAY off. That's why math problems go viral all the time, because they're simultaneously easy and yet so not.

Here are five problems that prove the point:

### 1. What's the Question Mark?

Let's start off super simple. Can you solve what number the question mark is supposed to be?

**The Answer:** 6.

**Explanation: **All of the rows and columns should add up to 15.

### 2. The Bat & The Ball

A bat and a ball cost one dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?

Was your answer 10 cents? That would be *wrong*!

**The Answer: **The ball costs 5 cents.

**Explanation:** When you read the math problem, you probably saw that the bat and the ball cost a dollar and ten cents in total and when you processed the new information that the bat is a dollar more than the ball, your brain jumped to the conclusion that the ball was ten cents without actually doing the math. But the mistake there is that when you actually do the math, the difference between $1 and 10 cents is 90 cents, not $1. If you take a moment to actually do the math, the only way for the bat to be a dollar more than the ball AND the total cost to equal $1.10 is for the baseball bat to cost $1.05 and the ball to cost 5 cents.

### 3. To Switch or Not to Switch

Imagine you're on a game show, and you're given the choice of three doors: Behind one door is a million dollars, and behind the other two, nothing. You pick door #1, and the host, who knows what's behind the doors, opens another door, say #3, and it has nothing behind it. He then says to you, "Do you want to stick with your choice or switch?"

So, is it to your best advantage to stick with your original choice or switch your choice?

Most people think the choice doesn't matter because you have a 50/50 chance of getting the prize whether you switch or not since there are two doors left, but that's actually not true!

**The Answer:** You should always switch your choice!

**The Explanation:** When you first picked one of the three doors, you had a 1 in 3 chance of picking the door with the prize behind it, which means you had a 2 in 3 chance of picking an empty door. What people get wrong here is thinking that because there are only two doors left in play, you have a 50% chance your first choice was correct. In actuality, your chances never changed.

There's still a 1 in 3 chance you picked the right door and a 2 in 3 chance you picked an empty door, which means that when the host opened one of the empty doors, he eliminated one of the WRONG choices and the chances that the prize is behind the last closed door is still 2 in 3 — double what the chances you picked the right door at first are. So, basically, by switching your door choice, you're betting on the 2 in 3 chance you picked the wrong door at first.

Sure, you aren't guaranteed to win if you switch, but if you play the game over and over, you'll win 2/3rds of the time using this method!

Still confused? Let the genius UC Berkeley math professor Lisa Goldberg explain it even better with a bunch of diagrams!

### 4. The PEMDAS Problem

When you do this seemingly simple problem, what is the answer you get?

The masses are split on the answer to this stumper. Some people are POSITIVE the answer is 1 and some people are absolutely sure the answer is 9.

**The Answer: **The winner is — 9!

**Explanation:** The handy order of operations rule you learned in grade school, PEMDAS, says you should solve a problem by working through the Parentheses, then the Exponents, the Multiplication and Division, followed by Addition and Subtraction. But the thing about PEMDAS is, some people interpret it different ways and in there lies the controversy behind this problem.

Some people think that anything *touching* a parentheses should be solved FIRST. Which means they simplify the problem as follows: 6÷2(1+2) = 6÷ 2(3) = 6÷6 = 1.

But just because a number is touching a parentheses doesn't mean it should be multiplied before division that's to the left of it. PEMDAS says to solve anything inside parentheses, then exponents, and then all multiplication and division *from left to right in the order both operations appear *(that's the key). That means that once you solve everything *inside* the parenthesis and simplify the exponents, you go from left to right no matter what. That means the problem should actually be solved as follows: 6÷2(1+2) = 6÷2*(1+2) = 6÷2*3 = 3*3 = 9.

### 5. The Lily Pad Problem

In a lake, there is a patch of lily pads. 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?

The tempting answer here is 24, but you're wrong if that's your final answer!

**The Answer:** The patch would reach half the size of the lake on day 47.

**Explanation:** With all the talk of doubling and halves, your brain jumps to the conclusion that to solve the problem of when the lily patch covers half the lake, all you have to do is divide the number of days it took to fill the lake (48) in half. It's understandable but wrong.

The problem says that the patch DOUBLES in size every day, which means that on any day, the lily patch was half the size the day before. So if the patch reaches the entire size of the lake on the 48th day, it means the lily pad was half the size of the lake on day 47.

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