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Number patterns

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**1**of**1**[ 7 posts ]Mona Pereth

Veteran

Joined: 11 Sep 2018

Age: 62

Gender: Female

Posts: 2,287

Location: New York City (Queens)

Mona Pereth wrote:

hurley4456 wrote:

synchromystic wrote:

hurley4456 wrote:

Can you complete the following pattern (next row in the sequence)....?

1

11

21

1211

111221

.................

1

11

21

1211

111221

.................

312211

13112221

1113213211

31131211131221

13211311123213112211

1113122113311213121113212221

311311222123211211131112311312113211

Very good!

For those interested in the recurcive pattern, you use the following rules:

- The successive row is derived from preceeding row (a given)

- By progessing from left to right, consider each number set as an individual element ( i.e. Row 5: 111, 22, and 1 are individual sets

- Count the number of elements per set and arrange left to right numerically ( i.e. Row 5: There exists three (3) 1's, two (2) 2's, and one (1) 1.

(312211) = row 6

I might have been able to see this pattern had I been shown maybe three or four more rows.

hurley4456 wrote:

I have another one, but this is derived from vedic mathematics, and I spent my some time working on it....Note: This is a visual pattern based on the shifting on numerical elements. Also, row N is supposed to be shifted to the right N-1 times (hint-space bar). So, if you write it out again by shifting row 2 one time, row 3 two times and so forth, it may help. This is is how you convert a square into an inverted triangle... You can explain verbally or visually based on preferree method..Consider the following term written as ABCD^(2)

3568^(2) =

09253664

306096

3680

48

3568^(2) =

09253664

306096

3680

48

The way you can preserve visual patterns in text, here on this message board, is by using the "code" tag, which among other things uses a monospaced font and preserves indentation. For example:

**Code:**

3568^(2) =

09253664

306096

3680

48

09253664

306096

3680

48

(Quote this message to see how to use the "code" tag.)

Anyhow, could you provide a few more examples of the pattern you are trying to show here?

Then hurley4456 posted the following additional examples of the pattern:

hurley4456 wrote:

**Code:**

For N = 1

6^(2) =

36

6^(2) =

36

**Code:**

For N = 2

26^(2) =

0436

36

26^(2) =

0436

36

**Code:**

For N = 3

894^(2) =

648104

14472

64

894^(2) =

648104

14472

64

**Code:**

For N = 5

12345^(2) =

0104091625

04122440

061630

0820

10

12345^(2) =

0104091625

04122440

061630

0820

10

_________________

- Autistic in NYC - Resources and new ideas for the autistic adult community in the New York City metro area.

- My life as one of the many belatedly-diagnosed autistic older people.

- Queens discussion group on Meetup.com.

Last edited by Mona Pereth on 10 Jul 2019, 9:13 pm, edited 1 time in total.

Mona Pereth

Veteran

Joined: 11 Sep 2018

Age: 62

Gender: Female

Posts: 2,287

Location: New York City (Queens)

Here, I see that hurley4456 deleted the above-quoted additional examples and posted the following instead:

hurley4456 wrote:

**Code:**

N = 1

5^(2) =

25

5^(2) =

25

**Code:**

N = 2

13^(2) =

0109

06

13^(2) =

0109

06

**Code:**

N = 3

246^(2) =

041636

1648

24

246^(2) =

041636

1648

24

**Code:**

N = 5

12345^(2) =

0103091625

04122440

061630

0820

10

12345^(2) =

0103091625

04122440

061630

0820

10

Hurley, are the previously-posted examples incorrect, or do you just think the newer ones are clearer?

Anyhow, in all these examples, I see that the first row consists of a sequence of two digit squares of the digits of the original number. I still can't figure out how the subsequent rows are derived. I'm not asking you to tell us yet, but maybe a few more examples might be helpful.

_________________

- Autistic in NYC - Resources and new ideas for the autistic adult community in the New York City metro area.

- My life as one of the many belatedly-diagnosed autistic older people.

- Queens discussion group on Meetup.com.

Mona Pereth wrote:

Here, I see that hurley4456 deleted the above-quoted additional examples and posted the following instead:

Hurley, are the previously-posted examples incorrect, or do you just think the newer ones are clearer?

Anyhow, in all these examples, I see that the first row consists of a sequence of two digit squares of the digits of the original number. I still can't figure out how the subsequent rows are derived. I'm not asking you to tell us yet, but maybe a few more examples might be helpful.

hurley4456 wrote:

**Code:**

N = 1

5^(2) =

25

5^(2) =

25

**Code:**

N = 2

13^(2) =

0109

06

13^(2) =

0109

06

**Code:**

N = 3

246^(2) =

041636

1648

24

246^(2) =

041636

1648

24

**Code:**

N = 5

12345^(2) =

0103091625

04122440

061630

0820

10

12345^(2) =

0103091625

04122440

061630

0820

10

Hurley, are the previously-posted examples incorrect, or do you just think the newer ones are clearer?

Anyhow, in all these examples, I see that the first row consists of a sequence of two digit squares of the digits of the original number. I still can't figure out how the subsequent rows are derived. I'm not asking you to tell us yet, but maybe a few more examples might be helpful.

Try the following...It will be easier to start with N = 2 or 3 where N = # of rows.

**Code:**

N= 2

49^(2) =

1681

72

............

2,401

49^(2) =

1681

72

............

2,401

**Code:**

369^(2) =

093681

3608

1

54

...........

136,161

093681

3608

1

54

...........

136,161

**Code:**

123^(2) =

010409

0412

06

...........

15,129

010409

0412

06

...........

15,129

synchromystic wrote:

I did it!!

I'll take a picture of my notes when I get home as that might be easier than trying to put it into words.

This was super fun, thank you hurley!

I'll take a picture of my notes when I get home as that might be easier than trying to put it into words.

This was super fun, thank you hurley!

I just realised I haven't actually solved it completely lol

I have worked out how the numbers in the triangle represent/can be used to calculate the square number,

*BUT*I haven't worked out how the numbers in the triangle are calculated beyond the first row.

Agh I got ahead of myself lol.

My notes showing how the triangle can be used to calculate the square.

synchromystic wrote:

synchromystic wrote:

I did it!!

I'll take a picture of my notes when I get home as that might be easier than trying to put it into words.

This was super fun, thank you hurley!

I'll take a picture of my notes when I get home as that might be easier than trying to put it into words.

This was super fun, thank you hurley!

I just realised I haven't actually solved it completely lol

I have worked out how the numbers in the triangle represent/can be used to calculate the square number,

*BUT*I haven't worked out how the numbers in the triangle are calculated beyond the first row.

Agh I got ahead of myself lol.

My notes showing how the triangle can be used to calculate the square.

Very interesting solution! I liked the way you color coded it...I do the same when creating plots in excel. You are on the right track by figuring out that the solution is derived using the tenths placement (zeroes).

The key is to figure out how each integer (substituted by A,B,C, and D) is shifted via two pair couples. So, I suggest you write out ABCD^(2) and determine the possible ways a pair (i.e AD, BD) can be shifted and then extract an ordered pattern. Also, find the mathematical operations (multiplucation, addition, exc) performed on the pairs. I hope this clarifies everything.

I realized it's for N = 5, but the same rule applies. Try to complete the orientation of all the remaining nodes. When they intersect, that means that the two digits are combined using a math operation (i.e. multiplication, exc). Once you figure out the operation, it should be no problem.

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