What is the pattern?

Logic Level 2

Given the following pyramid, what is the number of the next row?

1 1 1 1 1\quad 1 2 1 2 \quad 1 1 2 1 1 1\quad 2 \quad 1 \quad 1 1 1 1 2 2 1 1\quad 1 \quad 1 \quad 2 \quad 2 \quad 1

112123 122311 221122 312211

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2 solutions

Trick to solve this: Read out loud the number in the row. The speech will be the next number.

For example, 1 1 is read as " one number one ", so 11 11 will be the next number.

11 11 is read as " two number one ", so 21 21 will be the next number.

21 21 is read as " one number two , one number one ", so 1211 1211 will be the next number.

1211 1211 is read as " one number one , one number two , two number one ", so 111221 111221 will be the next number.

Applying the same method, 1112211 1112211 is read as " three number one , two number two , one number one ", so 312211 \boxed{312211} will be the answer.

Aaditya Pitke
Jul 30, 2015

In each row, 1 is added to both sides

Therefore next row will be 11112211

Now, sum of all consecutive 1s in a row is taken but the freshly added 1s are not counted.

Therefore final answer will be

1 1+1+1 22 11

First and last 1 will not be added as they are new

Therefore answer is 312211

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