# 17 Hard Math Problems That’ll Make Your Head Spin

## These brain-teasing hard math problems are tricky, but they’ll give your brain a workout—and they’re really rewarding when you figure one out!

## Time to test your brain!

These hard math problems aren’t straightforward arithmetic. They’ll challenge you to look at the “problems” a different way and test your logic and problem-solving skills while you’re solving. And if math isn’t your strong suit, take heart—most of these hard math problems just use very simple numbers with only basic operations—addition, subtraction, multiplication, and division. What makes them a challenge is often examining the problem to find out the “trick,” or the pattern and the way the numbers relate to one another. Others require a “fill-in-the-blank” technique that requires you to use trial and error and work backward. Time to put your brainpower to work! Maybe brush up on these easy math tricks you’ll wish you’d always known before you get started.

## Answer: Space 19

At first, it seems like this will take forever to figure out—but, in actuality, the runners will all be lined up after only six “moves”! Make a chart indicating where each runner will be after each “move.” To figure that out, all you really need to do is add! Just add the number of spaces each runner advances—three, two, one, and five—to the number they’re already at, going back to Space 1 after 30. Sure enough, they’ll all reach Space 19 at the same time. In the mood for something harder? Keep going—or try these difficult brain teasers that will leave you stumped.

## Ones and zeros

Below, you’ll see the binary notation for the decimal numbers 1 through 7. Following the pattern, what is the binary notation for the decimal number 12? Once you’ve solved this, brush up on some number facts you never knew before.

## Answer: 1100

If you went to five digits for this one, you did it wrong (and that’s OK; that’s what I did on my first attempt)! What makes this difficult, and different from most hard math problems, is that it’s so unlike how we’re used to looking at numbers, especially in a sequence. Basically, you’re moving through all of the numbers you can make with *just *ones and zeros, starting with the least (0, represented as four 0s) and getting greater. But you’ll always have four digits, so until you have a four-digit number (1000), the digit(s) to the left of the highest place will be a zero. So the question gives you up through 111 (written as 0111 to be four digits), and since it’s representing 7 and you’re trying to reach 12, just go through the next biggest numbers that use only 1s and 0s. So 8 will be 1000, 9 will be 1001, 10 will be 1010, 11 will be 1011, and 12 will be 1100.

## Answer: 1

Many of these hard math problems don’t require doing difficult math as much as they require identifying relationships between groups of numbers. In this case, don’t look at the horizontal rows of stamps but at the vertical pairs of stamps. The number in the ten’s place of the top stamp, divided by the number in the one’s place of the top stamp, equals the number on the bottom stamp (8 divided by 2 is 4 in the leftmost pair of stamps). So, for the last pair, 2 divided by 2 is 1.

## Energy saver

A transport company is greatly reducing the amount of oil it uses—but by how much? What number should be below the final barrel? Plus, try out these brain games that boost your brainpower.

## Answer: 2

Tricky—this one doesn’t require arithmetic at all! And thankfully, because those are some wacky, large numbers would not be fun to compute with. Instead, look for patterns in the numbers themselves. The following pattern presents itself: Each number (with the exception of the first, which is arbitrary) is the digits of the number before it, minus the first one, reversed. For instance, the first number is 19247. Take away the first digit, 1, and reverse it, and you get 7429—which, sure enough, is the second number. The number before the empty spot only has two digits, so when you remove the first one, 4, you’re left with just 2. No need to “reverse” a number with only one digit, so there’s your answer.