# Riddle: Add me to myself and multiply by 4. Divide me by 8 and you will have me once more. What number am I?

ANY NUMBER

## Explanation:

Our latest Riddle from our Riddle Robot Eyezak is specifically about math. Math can be fun, and can provide much enlightenment, and sometimes entertainment, to those who practice it. In our case, it can also provide a tricky Riddle that might not be as straight forward as it seems. Basically, we have a few parts of this Riddle that we have to solve:

• choose a number
• add the number to itself
• then divide it by 8
• verify that you still have the same original number

At first glance, this may seem like magic, but there is a hidden trick that can be used to determine the correct answer. First, we should analyze each part, then we will talk about the answer and a shortcut.

### Choose a Number

Pick a number, any number. For the purposes of this article, we will choose number 7. In the following sections of the article, we will apply the various mathematical operations to this number in an attempt to analyze how to come up with the correct answer to this Conundrum. Pay attention and read carefully, and you should see a clear reason that the answer is what it is.

So seven is our number. We need to add it to itself. It is important to point out, and for you to take note, that adding a number to itself is the same thing as multiplying the number by two. Therefore:

7 + 7 = 7 x 2

The answer to this part is:

7 x 2 = 14

Now that we have the answer to the “multiply times two” step, and we know that this step is actually “multiple times two,” we can move on to the next step.

Quadrupling a number means multiplying it by four. What we need to do now is take the 14 we had in our last section, and multiply that times 4. You can see this operation looks like so, when written in standard basic math syntax:

14 x 4 = ?

The answer to this easy operation is:

14 x 4 = 56

Most people will not need a calculator for this one, but in case you need to understand how to get it without a calculator, we will explain it quickly to you. An easy way to validate this is the right answer is to break this down into simpler operations. We can do this by breaking the 14 down, and then multiplying each part of that by 4, then later adding them together. This is what that looks like:

14 = ? + ?
14 = 10 + 4

10 x 4 = 40
4 x 4 = 16

40 + 16 = 56

As you can see, breaking them down into smaller operations makes it more clear how to achieve the answer, without a calculator. Next we need to divide by 8.

### Divide by 8

The Riddle says that our next step is to divide by 8. Effectively that means that we should take that 56 number from our last step, and divide that number by 8. Here is what that looks like:

56 / 8 = ?

Use a calculator to find that answer, because honestly the long division is super straight forward here and not worth explaining in depth:

56 / 8 = 7

Alright. Let us check the last step.

### Verify

The last step is to simply verify that the number we started with is the same as the number we ended with. Well, it is pretty easy for most Humans to verify that 7 is the same number as 7. Our Riddle answer has been verified. Seven is the answer to our riddle…. right?

Wrong. You probably chose a different number than we did. For argument’s sake, let us assume you chose the number 13. We should quickly check that 13 also works here:

13 x 2 = 26
26 x 4 = 104
104 / 8 = 13

Ah ha! We can see that the operations work for 13 also. We should try one more number just in case. This time we will choose something bigger. How about 4,974,173:

4,974,173 x 2 = 9,948,346
9,948,346 x 4 = 39,793,384
39,793,384 / 8 = 4,974,173

Okay. As you can see, it works for this arbitrarily large, random digit number we just made up! That must mean that this can work for ANY NUMBER! Test as many as you want, but trust us, it works for literally any number you can think of, and even any number you cannot think. This is simply because the math of it makes it so that it does not matter what number you choose. We should quickly review that.

### Shortcut

While you were reading this, remember when we said that it was important to note that “add a number to itself” is the same exact thing as “multiply times two?” This is important because that makes the operations look like this:

N x 2 = M
M x 4 = P
P / 8 = N

We can rephrase these equations a little differently, so that we can later condense them:

N x 2 = M
M x 4 = P
N x 8 = P

Now we can condense at least to of them via substitution:

N x 2 = M
M x 4 = P
is the same as:
(N x 2) x 4 = P

In this case, the parenthesis mean nothing, so we can remove them:

N x 2 x 4 = P

Now comparing the two remaining equations we can see that they look very similar:

N x 2 x 4 = P
N x 8 = P

If we condense these equations a little further, we see that they become identical:

N x 2 x 4 = P
is the same as:
N x (2 x 4) = P
which is the same as:
N x 8 = P

This leaves us with these two identical equations:

N x 8 = P
N x 8 = P

If we analyze what we did there, we can clearly see that the actual operations we performed were this:

N x (2 x 4) = N x 8

Because we multiply by N (the randomly selected number) on both sides, we can remove it from both sides through a process called canceling:

N x (2 x 4) = N x 8
(2 x 4) = 8

And as you can see, the resulting operation is simply a basic math identity: two times four equals eight.

This should be clear after you break it down like this; however if it is not, then please feel free to ask further questions in the comments below. Thanks for reading, and please pre-register for our app on Google Play Store or Apple App Store!

## One Last Thing: 