Conjecture about special grid of numbers

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Consider you have created grid of numbers like following image starting from any positive integer (in this case 8)

To create such grid, follow this steps;

1. Pick a number greater than one and write down $n, n-1, n-2, ..., 1$ as column headers


2. Likewise, write down $n, n-1, n-2, ..., 1$ as row headers


3. Fill each cell with $row_header * column_header$

If you group numbers diagonally starting from upper left, you get these groups of numbers

1. 64


2. 56, 56


3. 48, 49, 48


4. 40, 42, 42, 40


5. etc.

Let $G_n$ denote nth group. I want to prove if following theory is correct.
$$
i < k Rightarrow forall x in G_i, forall y in G_k, x > y
$$

It seems to hold for small enough starting numbers like $8$. It is trival to prove that any cell will be bigger then the cells to the right on the same row and will be bigger then the cells below it on the same column. But, I can't be sure about diagonal groups.

conjectures

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asked Jul 24 at 17:55

yasar

1674

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up vote
1
down vote

favorite

Consider you have created grid of numbers like following image starting from any positive integer (in this case 8)

To create such grid, follow this steps;

1. Pick a number greater than one and write down $n, n-1, n-2, ..., 1$ as column headers


2. Likewise, write down $n, n-1, n-2, ..., 1$ as row headers


3. Fill each cell with $row_header * column_header$

If you group numbers diagonally starting from upper left, you get these groups of numbers

1. 64


2. 56, 56


3. 48, 49, 48


4. 40, 42, 42, 40


5. etc.

Let $G_n$ denote nth group. I want to prove if following theory is correct.
$$
i < k Rightarrow forall x in G_i, forall y in G_k, x > y
$$

It seems to hold for small enough starting numbers like $8$. It is trival to prove that any cell will be bigger then the cells to the right on the same row and will be bigger then the cells below it on the same column. But, I can't be sure about diagonal groups.

conjectures

share|cite|improve this question

asked Jul 24 at 17:55

yasar

1674

add a comment | 

up vote
1
down vote

favorite

up vote
1
down vote

favorite

Consider you have created grid of numbers like following image starting from any positive integer (in this case 8)

To create such grid, follow this steps;

1. Pick a number greater than one and write down $n, n-1, n-2, ..., 1$ as column headers


2. Likewise, write down $n, n-1, n-2, ..., 1$ as row headers


3. Fill each cell with $row_header * column_header$

If you group numbers diagonally starting from upper left, you get these groups of numbers

1. 64


2. 56, 56


3. 48, 49, 48


4. 40, 42, 42, 40


5. etc.

Let $G_n$ denote nth group. I want to prove if following theory is correct.
$$
i < k Rightarrow forall x in G_i, forall y in G_k, x > y
$$

It seems to hold for small enough starting numbers like $8$. It is trival to prove that any cell will be bigger then the cells to the right on the same row and will be bigger then the cells below it on the same column. But, I can't be sure about diagonal groups.

conjectures

share|cite|improve this question

asked Jul 24 at 17:55

yasar

1674

Consider you have created grid of numbers like following image starting from any positive integer (in this case 8)

To create such grid, follow this steps;

1. Pick a number greater than one and write down $n, n-1, n-2, ..., 1$ as column headers


2. Likewise, write down $n, n-1, n-2, ..., 1$ as row headers


3. Fill each cell with $row_header * column_header$

If you group numbers diagonally starting from upper left, you get these groups of numbers

1. 64


2. 56, 56


3. 48, 49, 48


4. 40, 42, 42, 40


5. etc.

Let $G_n$ denote nth group. I want to prove if following theory is correct.
$$
i < k Rightarrow forall x in G_i, forall y in G_k, x > y
$$

It seems to hold for small enough starting numbers like $8$. It is trival to prove that any cell will be bigger then the cells to the right on the same row and will be bigger then the cells below it on the same column. But, I can't be sure about diagonal groups.

conjectures

share|cite|improve this question

asked Jul 24 at 17:55

yasar

1674

share|cite|improve this question

share|cite|improve this question

asked Jul 24 at 17:55

yasar

1674

asked Jul 24 at 17:55

yasar

1674

asked Jul 24 at 17:55

yasar

1674

1674

add a comment | 

add a comment | 

1 Answer
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accepted

Well, it's not true in the image you included. $8cdot3=24$ is one diagonal further up than $5cdot5=25$.

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answered Jul 24 at 18:05

joriki

164k10180328

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I feel pretty stupid now :)
  – yasar
  Jul 24 at 18:06
  

  
  
  
  

add a comment | 

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote



accepted

Well, it's not true in the image you included. $8cdot3=24$ is one diagonal further up than $5cdot5=25$.

share|cite|improve this answer

answered Jul 24 at 18:05

joriki

164k10180328

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I feel pretty stupid now :)
  – yasar
  Jul 24 at 18:06
  

  
  
  
  

add a comment | 

up vote
1
down vote



accepted

Well, it's not true in the image you included. $8cdot3=24$ is one diagonal further up than $5cdot5=25$.

share|cite|improve this answer

answered Jul 24 at 18:05

joriki

164k10180328

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I feel pretty stupid now :)
  – yasar
  Jul 24 at 18:06
  

  
  
  
  

add a comment | 

up vote
1
down vote



accepted

up vote
1
down vote



accepted

Well, it's not true in the image you included. $8cdot3=24$ is one diagonal further up than $5cdot5=25$.

share|cite|improve this answer

answered Jul 24 at 18:05

joriki

164k10180328

Well, it's not true in the image you included. $8cdot3=24$ is one diagonal further up than $5cdot5=25$.

share|cite|improve this answer

answered Jul 24 at 18:05

joriki

164k10180328

share|cite|improve this answer

share|cite|improve this answer

answered Jul 24 at 18:05

joriki

164k10180328

answered Jul 24 at 18:05

joriki

164k10180328

answered Jul 24 at 18:05

joriki

164k10180328

164k10180328

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I feel pretty stupid now :)
  – yasar
  Jul 24 at 18:06
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I feel pretty stupid now :)
  – yasar
  Jul 24 at 18:06
  

  
  
  
  

I feel pretty stupid now :)
– yasar
Jul 24 at 18:06

I feel pretty stupid now :)
– yasar
Jul 24 at 18:06

add a comment | 

 

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