Puzzles with numbers and things

[davis_greatest]

Well done Vidas!

Excellent! Nice solution, Vidas. Well done.

Slightly different from, but equallly valid to, the way I was hinting it could be done with the title "Snooker Tricolore" and the colours of the walls, ceiling and door being red, white and blue. You can colour the floor in a regular pattern with these three colours.

(T=toilet, r=red, w=white, b=blue - unfortunately I can't make the columns line up very neatly)

T r w b r w b r
r w b r w b r w
w b r w b r w b
b r w b r w b r
r w b r w b r w
w b r w b r w b
b r w b r w b r
r w b r w b r w

Each patch of cloth has to cover one red square, one white square, and one blue square. However, as there are 22 reds, 21 whites and 20 blues, rather than an equal number of each, you can also see that the covering cannot be done.

[April madness]

yes, i meant symmetrical pattern 8x8:
t 1 0 1 1 0 1 1
1 1 0 1 1 0 1 1
0 0 0 0 0 0 0 0
1 1 0 1 1 0 1 1
1 1 0 1 1 0 1 1
0 0 0 0 0 0 0 0
1 1 0 1 1 0 1 1
1 1 0 1 1 0 1 1

Cheers, Vidas, nice solution And hello from a snooker fan from Latvia

[Vidas]

yes, i meant symmetrical pattern 8x8:
t 1 0 1 1 0 1 1
1 1 0 1 1 0 1 1
0 0 0 0 0 0 0 0
1 1 0 1 1 0 1 1
1 1 0 1 1 0 1 1
0 0 0 0 0 0 0 0
1 1 0 1 1 0 1 1
1 1 0 1 1 0 1 1

[Robert602]

I believe that's just a typo, as the diagram is also 9 rows high. The lowest row of 0's should be omitted I believe, then it's right.

[davis_greatest]

Hi everyone,
we can divide all squares like this(t- toilet, 0&1 -free squares)

t 1 0 1 1 0 1 1
1 1 0 1 1 0 1 1
0 0 0 0 0 0 0 0
1 1 0 1 1 0 1 1
1 1 0 1 1 0 1 1
0 0 0 0 0 0 0 0
1 1 0 1 1 0 1 1
0 0 0 0 0 0 0 0
1 1 0 1 1 0 1 1

Any 3x1piece covers even number of "1" tiles (0 or 2).
but - there are 4x8+3=35 "1" tiles in total. So it's not possible.

What if I put a piece of cloth vertically along the left hand edge, starting one foot up from the bottom and finishing 4 feet up, so it covers 010 - that is exactly one "1" tile... an odd number?

[Robert602]

Hi everyone,
we can divide all squares like this(t- toilet, 0&1 -free squares)

t 1 0 1 1 0 1 1
1 1 0 1 1 0 1 1
0 0 0 0 0 0 0 0
1 1 0 1 1 0 1 1
1 1 0 1 1 0 1 1
0 0 0 0 0 0 0 0
1 1 0 1 1 0 1 1
0 0 0 0 0 0 0 0
1 1 0 1 1 0 1 1

Any 3x1piece covers even number of "1" tiles (0 or 2).
but - there are 4x8+3=35 "1" tiles in total. So it's not possible.

Wonderfully elegant solution Vidas. Looks right to me. Welcome to TSF .

[Vidas]

lol
OK, boils down to this, toilet stays, no tiling!
Cause, if you devide the original 64 squares into three types of sqares...

Hi everyone,
we can divide all squares like this(t- toilet, 0&1 -free squares)

t 1 0 1 1 0 1 1
1 1 0 1 1 0 1 1
0 0 0 0 0 0 0 0
1 1 0 1 1 0 1 1
1 1 0 1 1 0 1 1
0 0 0 0 0 0 0 0
1 1 0 1 1 0 1 1
0 0 0 0 0 0 0 0
1 1 0 1 1 0 1 1

Any 3x1piece covers even number of "1" tiles (0 or 2).
but - there are 4x8+3=35 "1" tiles in total. So it's not possible.

[Obligation]

Sorry no,

I actually thought I had done it, (honest) but then realised I had extended two 4x1. Doh!

[davis_greatest]

No scissors, no moving the toilet (unless you're prepared to pay for Mr Dotty's plumber).

If you believe you have done it, Obli, then please post it here. Perhaps you could use a different letter or symbol to represent each piece of cloth? E.g., it might start something like this (say):

AAABBBCD
EEEFFFCD
GGGHHHCD
....

[Obligation]

Ok!

The toilet is in the corner.

It is possible, and I have done it.


How shall I show you?

[Obligation]

AHAHAH!!!

Does the toilet HAVE to be in the corner?

[Obligation]

lol,

I meant 7x7.

And you are BOUND to leave two rows, one of which MUST be the row with the toilet, no?

[Semih_Sayginer]

yeah its possible, as long as hes got a pair of scissors

[davis_greatest]

Ok,

Not possible.

Cut the square into a 6x6 square and two rows - 8x1, 7x1

It is possible to arrange in a 6x6 (using 16 pieces), so we a left with rows of 7x1 and 8x1

By this point we have 5 pieces left.

We can lay down 4 more strips, and we are left with a square - 2x2.

Our remaining cloth is only 3x1.

I'm confused. 6x6 square with 16 pieces? Do you mean 7x7 square?

And you might be showing that IF you start with a 7x7 square, you will run into problems. But who said you have to start with a 7x7 square?

[snookersfun]

If you have some paint left from painting the door, ceiling and walls, can this help?

yes! Mix them all up, until you get the exact shade of green and paint the bl##dy final area, there!




(I know, you'll never get green that way)