Problem 215

[3n1gm4]

Why W(9,3) is just 8?

in the example there is:
3-2-2-2
2-2-3-2
3-3-3

and ok it has a running crack.

Now suppose these:

• 3-3-3
  2-2-3-2
  3-3-3
• 1-2-3-3
  2-2-3-2
  3-3-3
• 1-2-3-2-1
  2-2-3-2
  3-3-3
• 1-2-3-2-1
  2-2-3-2
  1-2-3-3
• 1-2-3-2-1
  2-2-3-2
  1-2-3-2-1
• 1-2-3-3
  2-2-3-2
  1-2-3-2-1
• 3-3-2-1
  2-2-3-2
  1-2-3-2-1
• 3-2-3-1
  2-2-3-2
  1-2-3-2-1
• 1-2-3-2-1
  2-2-3-2
  1-2-3-2-1

and I can go on... what am I missing?

PS: I hope notation is clear... numbers are for the width of the bricks, divided by lines...

[btilly]

There are only 2x1 and 3x1 bricks. There are no 1x1 bricks.

[3n1gm4]

There are only 2x1 and 3x1 bricks. There are no 1x1 bricks.

Good Point! Thank you

[thedon]

Problem 215 (View Problem)

Hello,

the problem #215 contains an example with a 9x3 wall where it says that “There are eight ways of forming a crack-free 93 wall, written W(9,3) = 8”. The weird thing is that I already found 12 possible ways; you can problably show me the 4 invalid ways and tell me why they're invalid.

Here are my walls (the numbers denote the width of each brick):

1.
3, 3, 3
2, 2, 2, 3
2, 2, 3, 2

2.
2, 2, 3, 2
2, 2, 2, 3
3, 3, 3

3.
3, 3, 3
2, 2, 2, 3
2, 3, 2, 2

4.
2, 3, 2, 2
2, 2, 2, 3
3, 3, 3

5.
3, 3, 3
2, 2, 2, 3
3, 2, 2, 2

6.
3, 2, 2, 2
2, 2, 2, 3
3, 3, 3

7.
2, 2, 3, 2
3, 3, 3
2, 3, 2, 2

8.
2, 3, 2, 2
3, 3, 3
2, 2, 3, 2

9.
3, 2, 2, 2
3, 3, 3
2, 2, 3, 2

10.
2, 2, 3, 2
3, 3, 3
3, 2, 2, 2

11.
3, 2, 2, 2
3, 3, 3
2, 3, 2, 2

12.
2, 3, 2, 2
3, 3, 3
3, 2, 2, 2

[jaap]

1.
3, 3, 3
2, 2, 2, 3
2, 2, 3, 2

#1: The bottom two rows both start with a 2 brick, so their right side form a crack.
#2: The top two rows both start with a 2.
#3: Bottom two rows both start with 2, and top two rows end with 3.
#4: Top two rows both start with 2, and bottom two rows end with 3.
#5: Top two rows end with 3.
#6: Bottom two rows end with 3.
#7: ok
#8: ok.
#9: Top two rows start with 3.
#10: Bottom two rows start with 3.
#11: ok
#12: Bottom two rows start with 3.

[thedon]

Now that's embarassing! After showing what's wrong I see it quite clearly. Thank you for pointing out the mistakes I made.

[mcsharma1990]

Please give hint for this problem.

[sivakd]

viewtopic.php?f=50&t=1428#p13426