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Maths - "look and say" Number Sequences











































The "look and say" sequence is an integer sequence.

The first integer is usually a single digit integer, it can be any positive integer.

Determine the next number in the sequence:

1
11
21
1211
111221
312211
?

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Feb 23, 2011
Maths - “look and say” Number Sequences
by: Staff

------------------------------------------
PART II


7th row: SEQUENCE UNKNOWN
work backwards

The sequence in the 6th (previous) row is known

Sixth (previous) row: 312211

Therefore, the verbal description of the 7th row should be:

Read as: “One 3”, “One 1”, “Two 2’s”, “Two 1’s”

Therefore, the number sequence for the 7th row is: 13 11 22 21


The final answer to your question is:

1
11
21
1211
111221
312211
13112221
.
.
.



For your information, there is an automatic way of calculating each row using a free on-line calculator. The calculator will also allow you to change the starting point (instead of using 1 for the first row, you can use 2, etc.

Just click on the link below:


http://www.btinternet.com/~se16/js/looknsay.htm





Thanks for writing.


Staff
www.solving-math-problems.com


Feb 23, 2011
Maths - “look and say” Number Sequences
by: Staff


The question:

1
11
21
1211
111221
312211
?

The answer:

PART I

This is a “look and say” number sequence

Read any row of numbers out loud. This will describe the previous row.

However, you must read each row a certain way.

With the exception of row 1, you have probably noticed that every row consists of “pairs of numbers”.

For example, row 5 consists of three pairs of numbers. These are: “11”, “12”, and “21”.

The first number in the sequence describes how many times the second number should be repeated in the previous row.

To find the sequence in row 4 (the previous row), read the pairs of numbers in row 5, one pair at a time.

11 should be read “one 1”
12 should be read “one 2”
21 should be read “two 1’s”

Row four (the previous row) is : 1211

The entire sequence can be developed as follows

1
This is the beginning of the sequence. It is not necessary to read the 1st row aloud.


11
Read the pairs of numbers in the 2nd row out loud to describe the 1st (previous) row.

The first number in each pair tells you how many times the second number in the pair appears in the previous row.

Number pairs: “11”
Read as: “One 1”

Row one (the previous row) is : 1


21
Read the pairs of numbers in the 3rd row out loud to describe the 2nd (previous) row.

The first number in each pair tells you how many times the second number in the pair appears in the previous row.

Number pairs: “21”
Read as: “Two 1’s”

Row two (the previous row) is : 11


1211
Read the pairs of numbers in the 4th row out loud to describe the 3rd (previous) row.

The first number in each pair tells you how many times the second number in the pair appears in the previous row.

Number pairs: “12”, and “11”
Read as: “One 2, One 1”

Row three (the previous row) is : 21


111221
Read the pairs of numbers in the 5th row out loud to describe the 4th (previous) row.

The first number in each pair tells you how many times the second number in the pair appears in the previous row.

Number pairs: “11”, “12”, and “21”

Read as: “One 1, One 2, Two 1’s”

Row four (the previous row) is : 1211


312211
Read the pairs of numbers in the 6th row out loud to describe the 5th (previous) row.

The first number in each pair tells you how many times the second number in the pair appears in the previous row.

Number pairs: “31”, “22”, and “11”

Read as: “Three 1’s, One 2’s, One 1”

Row five (the previous row) is : 111221


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