Our list of number sequence puzzles will put curious minds to the test.

Long a favorite of math teachers, sequence puzzles not only give your math abilities a workout but also your pattern recognition and critical thinking skills.

To get you started, here’s a simple one: 10, 20, 30, 40, __. What number comes next? The correct answer is 50. There’s a difference of ten between each number, so to arrive at the next number you add ten to 40 to get the answer, 50.

Oh, if only they were all so easy!

Let’s see what you got with these challenging number sequence puzzles.

## Number Sequence Puzzles Game

Are your pencils ready? Here come 8 puzzles ranging from fairly easy to very difficult. Good luck.

### 1.) What number comes next? 1, 3, 9, 27, 81, __?

Take the previous number and multiply by three to get the correct answer. 1 x 3 = 3, 3 x 3 = 9, and so on, until you arrive at 81 x 3 = 243.

Pro Tip: Look at the differences between the numbers in the sequence. If the numbers are going up in value, it’s likely that addition or multiplication is playing a role. When the number 9 jumped to 27, it clearly looked like a multiplier was in play.

### 2.) What number comes next? 1, 3, 4, 7, 11, __?

The next number is the sum of the previous two numbers. This sequence is famously known as the Fibonacci numbers and is perhaps the most famous sequence in mathematics.

Pro Tip: This sequencing pattern is prevalent in nature. The branching of a tree, the flowering of an artichoke, and the fruit sprouts of pineapple are just a few examples. The sequence is named after Leonardo Bonacci, or Fibonacci, an Italian mathematician from Pisa. He is widely considered to be “the most talented Western mathematician of the Middle Ages.”

Although Fibonacci made this sequence popular in the western world, it was used by Indian mathematicians as early as the 6th century.

### 3.) What number comes next? 8, 5, 4, 9, 1, _?

The numbers under ten are listed in alphabetical order: Eight, Five, Four, Nine, One, and then Seven. (The numbers Six, Ten, Three, and Two would complete the sequence).

Pro Tip: Ha! Just when you thought this was all about numbers and math, we throw in a little alphabet and spelling. Which brings us to this tip, when numbers fail you, what other type of order could the numbers be assembled in? Ask yourself this question when you’re stuck.

### 4.) What number comes next? 2, 3, 5, 7, 11, _?

The sequence is a list of prime numbers — numbers that are only divisible by one and the number itself. The number four is divisible by 1,2, and 4, which makes it not a prime number. Since the number five is divisible by only one and five, it is a prime number.

Pro Tip: I’m not going to lie. This was a tough one. As with the previous tip, when all else fails, consider any similarities the numbers as a group have. You might have noticed that the number 2 is the only even number. It is also the only even prime number — because even numbers are divisible by 2.

### 5.) What number comes next? 0, 5, 3, 8, 6, _?

So, to solve this puzzle, look hard at the differences in the numbers from one to the next. You’ll note a pattern of +5; -2. To get from 0 to five, you +5, then you take away 2 to get to 3. Add five to get to eight, and minus 2 to get to six. From six, you add five to get to the answer of eleven.

Pro Tip: When the going gets tough, sometimes it pays to think of two sets of sequences going on. For example, the first, third, and fifth numbers might follow one pattern, while the second, fourth, and sixth numbers follow another.

### 6.) What number comes next? 68, 36, 20, 12, 8, _?

In this sequence, two operations are performed on the next number. First, we divide by 2, and then we add 2. So, 68 divided by 2 = 34, and then add 2 for 36. With the number 8, we divide by 2 to get to a subtotal of 4 and then add 2 for the solution: 6.

Pro Tip: Look at multiple operations happening to the same number. Here it was division and addition.

### 7.) What number comes next? 1, 3, 6, 10, 15, __?

Arrive at this answer by increasing the difference between the previous and next number by one. The difference between one and three is 2, the difference between three and six is 3, the difference between six and ten is 4, and the difference between ten and fifteen is five, so the difference between 15 and the solution must be 6. That makes the only answer 21!

Pro Tip: Writing down the difference between each number sometimes brings the solution immediately to light.

### 8.) What number comes next? 3, 3, 5, 4, 4, _? (NOTE: Difficulty level: Super Hard!)

Bravo to the folks who answer this correctly. This riddle combines numeric order with the spelling of numbers. One (3 letters), Two (3 letters), Three (5 letters), Four (4 letters), Five (four letters), and Six (three letters).

Pro Tip: Sometimes, you need to be lucky to arrive at the correct solution.

## Scoring for Pattern Recognition

Since this test was so difficult, the curve indicates the following:

Answered 4 or more correctly: Sequence Superstar.

Answered 2 – 3 correctly: Well Done.

Oops, Answered less than 2 correctly: Don’t worry, you know what to look for now.

By Mike O’Halloran

Mike is the co-founder of ListCaboodle and the co-author of four trivia books for kids.

Encore

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