Tiling a $3times 4$ rectangle with $1times 2$ tiles. [closed]

Clash Royale CLAN TAG#URR8PPP

up vote
-3
down vote

favorite

A 3 unit by 4 unit area on a wall is to be tiled with 1 unit by 2 unit
tiles. The diagram below shows two possible patterns for the tiling.

In how many different ways is it possible to tile the area?

combinations

share|cite|improve this question

edited Jul 22 at 22:06

amWhy

189k25219431

asked Jul 22 at 21:57

geetha

585

closed as off-topic by amWhy, Xander Henderson, Shailesh, Leucippus, Parcly Taxel Jul 23 at 1:45

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, Shailesh, Leucippus, Parcly Taxel

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Try counting them one by one assuming all 2 by 1 tiles to be,say, horizontal initially to find the number of ways they could arranged.
  – Pi_die_die
  Jul 22 at 22:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Reduce number of cases by observing that outside vertical line can only have 1 whole and half a tile OR 3 half tiles ...this observation reduces some cases
  – Pi_die_die
  Jul 22 at 22:11
  

  
  
  
  

add a comment | 

up vote
-3
down vote

favorite

A 3 unit by 4 unit area on a wall is to be tiled with 1 unit by 2 unit
tiles. The diagram below shows two possible patterns for the tiling.

In how many different ways is it possible to tile the area?

combinations

share|cite|improve this question

edited Jul 22 at 22:06

amWhy

189k25219431

asked Jul 22 at 21:57

geetha

585

closed as off-topic by amWhy, Xander Henderson, Shailesh, Leucippus, Parcly Taxel Jul 23 at 1:45

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, Shailesh, Leucippus, Parcly Taxel

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Try counting them one by one assuming all 2 by 1 tiles to be,say, horizontal initially to find the number of ways they could arranged.
  – Pi_die_die
  Jul 22 at 22:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Reduce number of cases by observing that outside vertical line can only have 1 whole and half a tile OR 3 half tiles ...this observation reduces some cases
  – Pi_die_die
  Jul 22 at 22:11
  

  
  
  
  

add a comment | 

up vote
-3
down vote

favorite

up vote
-3
down vote

favorite

A 3 unit by 4 unit area on a wall is to be tiled with 1 unit by 2 unit
tiles. The diagram below shows two possible patterns for the tiling.

In how many different ways is it possible to tile the area?

combinations

share|cite|improve this question

edited Jul 22 at 22:06

amWhy

189k25219431

asked Jul 22 at 21:57

geetha

585

A 3 unit by 4 unit area on a wall is to be tiled with 1 unit by 2 unit
tiles. The diagram below shows two possible patterns for the tiling.

In how many different ways is it possible to tile the area?

combinations

share|cite|improve this question

edited Jul 22 at 22:06

amWhy

189k25219431

asked Jul 22 at 21:57

geetha

585

share|cite|improve this question

share|cite|improve this question

edited Jul 22 at 22:06

amWhy

189k25219431

edited Jul 22 at 22:06

amWhy

189k25219431

edited Jul 22 at 22:06

amWhy

189k25219431

189k25219431

asked Jul 22 at 21:57

geetha

585

asked Jul 22 at 21:57

geetha

585

asked Jul 22 at 21:57

geetha

585

585

closed as off-topic by amWhy, Xander Henderson, Shailesh, Leucippus, Parcly Taxel Jul 23 at 1:45

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, Shailesh, Leucippus, Parcly Taxel

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by amWhy, Xander Henderson, Shailesh, Leucippus, Parcly Taxel Jul 23 at 1:45

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, Shailesh, Leucippus, Parcly Taxel

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Try counting them one by one assuming all 2 by 1 tiles to be,say, horizontal initially to find the number of ways they could arranged.
  – Pi_die_die
  Jul 22 at 22:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Reduce number of cases by observing that outside vertical line can only have 1 whole and half a tile OR 3 half tiles ...this observation reduces some cases
  – Pi_die_die
  Jul 22 at 22:11
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Try counting them one by one assuming all 2 by 1 tiles to be,say, horizontal initially to find the number of ways they could arranged.
  – Pi_die_die
  Jul 22 at 22:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Reduce number of cases by observing that outside vertical line can only have 1 whole and half a tile OR 3 half tiles ...this observation reduces some cases
  – Pi_die_die
  Jul 22 at 22:11
  

  
  
  
  

Try counting them one by one assuming all 2 by 1 tiles to be,say, horizontal initially to find the number of ways they could arranged.
– Pi_die_die
Jul 22 at 22:04

Try counting them one by one assuming all 2 by 1 tiles to be,say, horizontal initially to find the number of ways they could arranged.
– Pi_die_die
Jul 22 at 22:04

Reduce number of cases by observing that outside vertical line can only have 1 whole and half a tile OR 3 half tiles ...this observation reduces some cases
– Pi_die_die
Jul 22 at 22:11

Reduce number of cases by observing that outside vertical line can only have 1 whole and half a tile OR 3 half tiles ...this observation reduces some cases
– Pi_die_die
Jul 22 at 22:11

add a comment | 

2 Answers
2

active

oldest

votes

up vote
1
down vote

Hint: each vertical side can contain 3 horizontal tiles or 1 horizontal and 1 vertical tiles

share|cite|improve this answer

answered Jul 22 at 22:12

Martín Vacas Vignolo

3,418421

• 
  
  
  

  
  

  
  
  
  
  
  

  
  What's a "vertical side"?
  – amWhy
  Jul 22 at 22:19
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @amWhy a "height" of rectangle
  – Martín Vacas Vignolo
  Jul 22 at 22:21
  

  
  
  
  

add a comment | 

up vote
0
down vote

Cut the $3times4$ rectangle into two $3times 2$ rectangles. In each of these $3times 2$ rectangles, there must be:

• A horizontal tile on the top or bottom row


• A $2times2$ square made up of either two horizontal or two vertical tiles covering the other two rows

There are two exceptions to these rules. The first is your right-hand example, the other is that rotated $180^0$.

You simply need to work out/count how many ways you can adhere to these rules (not forgetting there are two halves) then simply add $2$ to your answer to account for the exceptions.

share|cite|improve this answer

answered Jul 22 at 22:30

Rhys Hughes

3,8681227

add a comment | 

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote

Hint: each vertical side can contain 3 horizontal tiles or 1 horizontal and 1 vertical tiles

share|cite|improve this answer

answered Jul 22 at 22:12

Martín Vacas Vignolo

3,418421

• 
  
  
  

  
  

  
  
  
  
  
  

  
  What's a "vertical side"?
  – amWhy
  Jul 22 at 22:19
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @amWhy a "height" of rectangle
  – Martín Vacas Vignolo
  Jul 22 at 22:21
  

  
  
  
  

add a comment | 

up vote
1
down vote

Hint: each vertical side can contain 3 horizontal tiles or 1 horizontal and 1 vertical tiles

share|cite|improve this answer

answered Jul 22 at 22:12

Martín Vacas Vignolo

3,418421

• 
  
  
  

  
  

  
  
  
  
  
  

  
  What's a "vertical side"?
  – amWhy
  Jul 22 at 22:19
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @amWhy a "height" of rectangle
  – Martín Vacas Vignolo
  Jul 22 at 22:21
  

  
  
  
  

add a comment | 

up vote
1
down vote

up vote
1
down vote

Hint: each vertical side can contain 3 horizontal tiles or 1 horizontal and 1 vertical tiles

share|cite|improve this answer

answered Jul 22 at 22:12

Martín Vacas Vignolo

3,418421

Hint: each vertical side can contain 3 horizontal tiles or 1 horizontal and 1 vertical tiles

share|cite|improve this answer

answered Jul 22 at 22:12

Martín Vacas Vignolo

3,418421

share|cite|improve this answer

share|cite|improve this answer

answered Jul 22 at 22:12

Martín Vacas Vignolo

3,418421

answered Jul 22 at 22:12

Martín Vacas Vignolo

3,418421

answered Jul 22 at 22:12

Martín Vacas Vignolo

3,418421

3,418421

• 
  
  
  

  
  

  
  
  
  
  
  

  
  What's a "vertical side"?
  – amWhy
  Jul 22 at 22:19
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @amWhy a "height" of rectangle
  – Martín Vacas Vignolo
  Jul 22 at 22:21
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  What's a "vertical side"?
  – amWhy
  Jul 22 at 22:19
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @amWhy a "height" of rectangle
  – Martín Vacas Vignolo
  Jul 22 at 22:21
  

  
  
  
  

What's a "vertical side"?
– amWhy
Jul 22 at 22:19

What's a "vertical side"?
– amWhy
Jul 22 at 22:19

@amWhy a "height" of rectangle
– Martín Vacas Vignolo
Jul 22 at 22:21

@amWhy a "height" of rectangle
– Martín Vacas Vignolo
Jul 22 at 22:21

add a comment | 

up vote
0
down vote

Cut the $3times4$ rectangle into two $3times 2$ rectangles. In each of these $3times 2$ rectangles, there must be:

• A horizontal tile on the top or bottom row


• A $2times2$ square made up of either two horizontal or two vertical tiles covering the other two rows

There are two exceptions to these rules. The first is your right-hand example, the other is that rotated $180^0$.

You simply need to work out/count how many ways you can adhere to these rules (not forgetting there are two halves) then simply add $2$ to your answer to account for the exceptions.

share|cite|improve this answer

answered Jul 22 at 22:30

Rhys Hughes

3,8681227

add a comment | 

up vote
0
down vote

Cut the $3times4$ rectangle into two $3times 2$ rectangles. In each of these $3times 2$ rectangles, there must be:

• A horizontal tile on the top or bottom row


• A $2times2$ square made up of either two horizontal or two vertical tiles covering the other two rows

There are two exceptions to these rules. The first is your right-hand example, the other is that rotated $180^0$.

You simply need to work out/count how many ways you can adhere to these rules (not forgetting there are two halves) then simply add $2$ to your answer to account for the exceptions.

share|cite|improve this answer

answered Jul 22 at 22:30

Rhys Hughes

3,8681227

add a comment | 

up vote
0
down vote

up vote
0
down vote

Cut the $3times4$ rectangle into two $3times 2$ rectangles. In each of these $3times 2$ rectangles, there must be:

• A horizontal tile on the top or bottom row


• A $2times2$ square made up of either two horizontal or two vertical tiles covering the other two rows

There are two exceptions to these rules. The first is your right-hand example, the other is that rotated $180^0$.

You simply need to work out/count how many ways you can adhere to these rules (not forgetting there are two halves) then simply add $2$ to your answer to account for the exceptions.

share|cite|improve this answer

answered Jul 22 at 22:30

Rhys Hughes

3,8681227

Cut the $3times4$ rectangle into two $3times 2$ rectangles. In each of these $3times 2$ rectangles, there must be:

• A horizontal tile on the top or bottom row


• A $2times2$ square made up of either two horizontal or two vertical tiles covering the other two rows

There are two exceptions to these rules. The first is your right-hand example, the other is that rotated $180^0$.

You simply need to work out/count how many ways you can adhere to these rules (not forgetting there are two halves) then simply add $2$ to your answer to account for the exceptions.

share|cite|improve this answer

answered Jul 22 at 22:30

Rhys Hughes

3,8681227

share|cite|improve this answer

share|cite|improve this answer

answered Jul 22 at 22:30

Rhys Hughes

3,8681227

answered Jul 22 at 22:30

Rhys Hughes

3,8681227

answered Jul 22 at 22:30

Rhys Hughes

3,8681227

3,8681227

add a comment | 

add a comment |