Think Outside the Box to Find the Next Number in This Sequence

Does this unusual sequence have you stumped?

I’m going to give you some hints to see if you can find the trick before I reveal it. If you just want to check your answer, scroll to the bottom of the page.

Hint #1: Think outside the box. It’s not all about mathematical calculations.

Hint #2: Try saying the sequence out loud.

Hint #3: Read the digits instead of the numbers

Solution: This sequence is called the look-and-say sequence. The digits work in pairs and relate to the previous number in the sequence. Written differently, it looks like this:

The first digit in each pair indicates the number of each digit contained in order in the previous number. To find the next number in the sequence, look at the previous number and say how many of a particular digit there are.

The next number in the sequence is: 31131211131221, otherwise known as three 1s, one 3, one 2, one 1, one 3, one 2, two 1s.

Interestingly, the digits in the sequence can never be higher than 3. A 4 would require there to be four of the same digit in a row, which would indicate an error in the previous number. We can think about it backwards. If you have, for example, 1111 (which is what would create your 41 or four 1s), then there would have been 11 in the previous number. However, you would have called that 21 (or two 1s) rather than 1111 (one 1 one 1).

Try one of our other puzzles: Can You Solve This Centuries-Old Math Problem?