Puzzles with numbers and things

[davis_greatest]

Congratulations Monique! Nice pictures

Everyone has got quite different pictures - abextra and snookersfun, please would you put yours up too.

Below was my drawing for round 293, the 12x12 chessboard.

Round 294 now closed

I have received answers by private message to round 294 from snookersfun, abextra and Monique, so we'll close that round too. Please would you put up your drawings for the smallest possible odd chessboard that Charlie found, using 4 colours.

As described in a number of different ways in the answers I received, it is impossible for Gordon to colour in an odd number chessboard using 147 colours. This is because if the number of colours is divisible by 3, as 147 is, the number of squares coloured would always be even, whereas an odd chessboard has an odd number of squares. The 1st & 2nd shape combined equal the 3rd shape, the 4th and 5th combined equal the 6th, the 7th and 8th combined equal the 9th etc. - so an even number of squares is coloured after every 3rd colour, no matter what the size of the initial shapes.

[Monique]

R292 also

R292Sol.bmp

with 2 yellows and 7 greens

[Monique]

R293 follow up

And here it is ....

R293-6-8.bmp

[Monique]

R293 ...

R293.3-10.bmp

Here is a solution (if I'm not confused once again ...) with 3 yellows and 10 greens.
Now looking for one with 6 yellows and 8 greens.

[davis_greatest]

... and snookersfun meanwhile has sent a correct answer to round 294! Well done!

That means that both abextra and snookersfun have solved all the snooker chessboard questions so far (rounds 291 to 294) and Monique has done round 291 so far (was obviously too busy with those crazy spoons!)

So (and in response to a request for more time!), we'll leave rounds 292 to 294 open until 9a.m. GMT Thursday, 3 January 2008 or until the next person solves them, whichever is the sooner.

Anyone wanting to answer before that time, please post answers directly on the thread. After that, or earlier if anyone else has posted correct answers before then, would abextra and snookersfun please post their answers up here.

One last snooker chessboard (for now) from the Nugget - and then he or I will think of something else ....

Round 295 - A big outdoor chessboard

Davis has now found, on his Brentwood estate, a rather large patch of land that he would like to be coloured in, using the six snooker colours, just as in rounds 291 to 293.

This time, the patch is a square of 1470 rows (i.e. a 1470 x 1470 "chessboard")!

This being quite a challenge, he comes to Oliver, who can solve any puzzle (if it is possible to do so) and Steve asks Oliver whether he can colour it.

What is Oliver's response - "yes" or "no"? (And you must give an explanation - either a proof that it can be done or a proof that it cannot!)

[snookersfun]

...and coming back, I found a perfect solution to the very hard spoon question (R.290) from Monique now. Very well done!

[davis_greatest]

Round 292 breaking news

... and now abextra has joined snookersfun and added round 292 (the 10x10 chessboard) to the Completed list. That was a tough round - well done!

[davis_greatest]

Round 294 newsflash

abextra is now the first in with an answer to round 294 - so congratulations to abextra, Charlie and Gordon!

[davis_greatest]

Round 293 update

Meanwhile, abextra has provided two different possible colourings for round 293, the 12x12 chessboard! Well done! We'll leave it open a little longer, before inviting the colourings to come on the thread.

[davis_greatest]

Nice paints, April Now pour them on the chessboard

We'll leave rounds 292 and 293 open, as I think a couple of people may still be working on them. But, so as not to delay, another chessboard question! ....

Round 294 That's odd

So... we've had boards of 8x8, 10x10 and 12x12! All even (i.e. even number of rows).

The Nugget has got a bit bored with every board so far being even - in fact, he found it a bit odd that they were all even - so, to even things out, he decides to stop colouring in an even board and look for an odd board, so he won't get bored with the next board. How odd!

He has also found that using the six colours from snooker every time is making him loopy, so he decides that from now on, different numbers of colours can be used - not necessarily six.

As always, the first two shapes can be any size. After that, it must be possible to make every shape by sticking together the two previous shapes. Rotating or flipping the shapes over (reflecting them) is permitted, just as before.

He gets out lots of paints but, so there won't be any monkey business, he pops around to my house, as he often does, and asks my pet apes to help him out.

First, he asks Charlie to colour in the smallest possible square board he can, with an odd number of rows. The only thing that he stipulates is that Charlie must use at least 3 colours, otherwise it would be too easy!

Then, the Nugget asks Gordon to colour in a square board with an odd number of rows, as many rows as Gordon likes, but Gordon must use exactly 147 colours!

What possible answers do Charlie and Gordon, each being very smart and able to solve any puzzle, give?

[April madness]

just needs to add the colours

The best ones I could get...

[davis_greatest]

First in with perfect answers to rounds 292 and 293 is snookersfun. Congratulations! For round 293 (the 12x12 chessboard), snookersfun has found solutions for two different sizes for the yellow (and hence every other colour).

Congratulations to semih too for an almost perfect answer above - just needs to add the colours and it will be perfect.

[Semih_Sayginer]

was just checking that you can use the address of the attatched image to show the bigger illustration.

(imagine it can be done in preview by taking the address from there)

[davis_greatest]

Edited post: for anyone who read the earlier post about round 292 - it is definitely possible, so I've deleted the earlier post where I said I hadn't yet got a solution (as I did finally find one!)

[davis_greatest]

And may as well add at the same time as the spoons and round 292,

Round 293 Oversized CheckmateApe

Exactly the same as rounds 291 and 292, but with a 12x12 chessboard to colour...

Round 291 Checkmate

While Ronnie is counting the dots on his spoons, Steve Davis is keeping his brain alert and redesigning his chessboard to make it more Interesting. He decides that, instead of the boring black and white pattern, it would look better with some snooker colours.

So, he scrubs out the black squares and then colours in the chessboard in six different patches - coloured in order: yellow, green, brown, blue, pink and black.

Each patch is a different shape, bigger than the previous one, and consists of squares of the chessboard connected by one or more edges (not just at a corner).

First, Steve colours in the yellow and green patches wherever he likes. After that, the shape of each patch can be made by sticking together the shapes of the two previous ones (rotations are allowed). For example, sticking together the yellow and green patches forms the shape of the brown one; sticking together the green and brown patches forms the shape of the blue one, etc.

Help Steve colour in his snooker chessboard (all squares must be coloured - click on thumbnail to enlarge).