Some of the most challenging number puzzles require very little mathematical knowledge. In fact, the puzzle below requires some non-mathematical thinking to solve. I’m not sure when or where I first came across this sequence, but it must have been in middle school. But after some more research, I discovered that mathematician John Horton Conway wrote a playful paper about this pattern and its variations in a Cambridge University student magazine. He’s a recreational math enthusiast and is famous for his zero-player Game of Life. EurekaThe puzzles are deceptively difficult, combining generative complexity with a simple solution that makes for a fun sequence to solve and share.
So, without further ado, what comes next in this pattern?
The next line is 13112221 followed by 1113213211. Any theories on how this works?
Read on to find out more…
This pattern is known as a “see and say” sequence because for each entry you read out loud and write down what you saw on the previous line.
Because the sequence starts with 1, the next row is “one 1” (aka 11), the next row is “two 1s” (aka 21), then “one 2, one 1” (aka 1211), and so on. This pattern never gets beyond 1, 2, 3. Do you know why? And what happens if we introduce other starting digits?
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