Problem #15 EASY
The Patterns in the Sequence
Adobe Pattern Recognition Math
Problem Statement
Look closely at the following sequence of numbers:
1, 11, 21, 1211, 111221, 312211, ...
What is the next number in this sequence, and what is the underlying logic that generates it?
Answer & Quick Explanation
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The next number is 13112221. The sequence is the Look-and-Say sequence, where each term describes the digits of the previous term.
Detailed Editorial Solution
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This is the famous Look-and-Say sequence, discovered by mathematician John Conway. Each term is generated by "reading" the digits of the previous term.
Let's walk through it:
- **1** is read as "one 1" → **11**
- **11** is read as "two 1s" → **21**
- **21** is read as "one 2, one 1" → **1211**
- **1211** is read as "one 1, one 2, two 1s" → **111221**
- **111221** is read as "three 1s, one 2, two 1s" → **312211**
- **312211** is read as "one 3, one 1, two 2s, two 1s" → **13112221**
Therefore, the next number is 13112221.