There aren’t many of us out there who can resist a good brain challenge—add a few balloons onto the equation, and we’re hooked! This one has gone viral and has been circulating the internet recently, and it’s even gotten some math PhDs interested.

Take a look at the balloon math problem below, and using the given equations, see if you can solve the last question.

Can you figure out the answer?

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Take a moment or two to work it out in your head or on paper—this will be a good opportunity to take a much-deserved break from all that hard work you’ve been doing and refocus your mind with some math before getting on with your day.

When you think you have found the solution, check down below for an explanation and the final answer.

First of all, let’s break down the problem line by line and solve each part of the equation. That should allow us to solve the final equation.

In the first equation, we have 1 red balloon plus 1 red balloon plus 1 red balloon, which equals 30. **That means that each red balloon must be equal to 10.**

In the second equation, we see that 1 red balloon plus 2 yellow balloons plus 2 yellow balloons equals 18. Since we’ve established that 1 red balloon equals 10, we can subtract that from both sides of the equation, and we now know that 2 yellow balloons plus 2 yellow balloons equals 8. **Therefore, 2 yellow balloons must equal 4.**

Thirdly, we have 2 yellow balloons minus 2 green balloons, which equals 2. Because we now know that 2 yellow balloons equals 4, we can now determine that **2 green balloons must equal 2.**

Now, we have the value of *all* of the balloons, and so we are able to solve the last equation.

Thus, we may solve the fourth equation, 1 green balloon plus 1 red balloon multiplied by 1 yellow balloon.

From the first three equations, we learned that 2 yellow balloons equals 4, and 2 green balloons equals 2. It therefore seems reasonable that 1 yellow balloon should equal 2, and 1 green balloon should equal 1.

Also, you need to remember that there is an **order of operations** for solving addition and multiplication; *numbers multiplied by each other have to be solved first* or the answer will be incorrect.

Ten multiplied by 2 equals 20, plus 1 equals 21. **The answer is 21.**

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Were you able to solve this math problem? Admit it, it was the balloons that grabbed your interest, right? Nevertheless, you probably found solving this puzzle at least a little bit satisfying. That’s because your brain loves putting puzzles together and solving problems—not to mention all the bragging rights that come with it!

***If you’re wondering why this puzzle would garner interest from math PhDs, check out this video (it will likely drive you crazy with its sophisticated math lingo:)**

**BONUS: Are you up for an even bigger challenge? Try this one on for size!**

## Can You Solve the Sequence? There Are 2 Solutions (But You’ll Need an IQ of 130+)

Now some of you skeptics might be looking at this mind bender and thinking: “The answer is 19. It makes no difference that two of the previous equations are wrong.” And as far as we’re concerned, you’re correct in thinking that! If you declare 19 to be your answer, we’ll take it. That’s thinking outside of the box!

But for those who really want to test their metal, this mind bender has a few more tricks up its sleeve, as you’ll see.

There are a couple of hidden patterns in the sequence of equations that ties it all together and gives you the real answer. But you’ll have to figure out that pattern and solve it mathematically. Are you up for it?

**Let’s take another look:**

Take a moment to consider what patterns are at work. Hint: there are two possible solutions (besides the aforementioned trick answer of 19). Try to come up with *both *solutions before you scroll down to see the answers below.

**Solution 1 Answer:**

The first equation makes plain sense: 1 + 4 = 5 , naturally. But that’s where the logic seems to end. The second and third equations, 2 + 5 = 12 and 3 + 6 = 21, do not equate unless there is a larger pattern or hidden rule that we aren’t given in the sequence. If we can determine what that is, we may be able to solve the last equation.

**The Pattern:**

Add the left side of any given equation to the answer of the previous equation (as per the illustration below). In the case of the first equation, there is no previous equation, and so you would add zero to the left side of the equation (0 + 1 + 4), which gives you 5. The same pattern works for the second and third equations, and so we know it’s correct. Apply this rule to the last equation, and we get the solution.

**The answer for Solution 1 is 40.**

Following this pattern, we can solve the final equation by adding the previous answer (21) to the left side of the said equation (8 + 11) which gives us 40.

**Solution 2 Answer:**

You might have thought that that is all there is to it, but in fact, as some of you may have noticed, there is another pattern hidden in the sequence, and it gives a *second solution* that also works. It uses the first pattern but results in a different, yet perfectly valid, answer.

**The Second Pattern:**

Observe how the first number from each of the first three equations creates a *consecutive* sequence: 1, 2, 3; and how the second number from each of the first three equations creates another *consecutive* sequence: 4, 5, 6.

The last equation may seem to break this consecutive pattern, but in fact, it fits into the sequence *if you grant that parts of that sequence exist but are omitted from view*, as per the illustration below:

And since the entire sequence has now changed—including the second-last equation in particular—and supposing we use the same rule as Solution 1 to solve the last equation, we will get a different answer, as you can see from the illustration below:

**And the answer for Solution 2 is 96!**

*Photo Credit: Illustration – The Epoch Times*