Puzzles with numbers and things

[abextra]

R.393: separating
... Charlie's plan is to separate at least pink and black by not having them on neighbouring spots, and see if that will show a difference in play.

So, how many different ways are there to do that? Out of how many different ways to arrange all colours on those spots without those constrictions?

... ... and time to close that round, if anybody feels like putting up his solution with a short explanation...

Well, in total there are 720 different ways to arrange six colours on six spots and Charlie has 432 ways to arrange the balls such way that black and pink are not on the neighbouring spots. I haven't found all the unique solutions yet...

[Monique]

Just to be 100% certain I suppose the "path" must "reach" the balls at right angles as well, not diagonally? (meaning there are max 4 possble access squares around each ball not 8)

[snookersfun]

Just to be 100% certain I suppose the "path" must "reach" the balls at right angles as well, not diagonally? (meaning there are max 4 possble access squares around each ball not 8)

yes, that is correct
and update: first one solving both 'joiners' was moglet yesterday, and Mon has sent a perfect 1st one today morning (and the 2nd one right now as well). Congratulations moglet and Monique!

oh, and thank you abextra!
...and by now Abextra has joined the colours as well, well done!

[snookersfun]

update to R. 394: solved by d_g now, too! Well done!

and with that to
R.395: Singles and Pairs

In the following imagine again a part of a snooker table. You are supposed to fill the whole grid (consisting of pairs or single slots) with snooker-balls of three colours, white, black and red.
The following restrictions apply: white balls come only in pairs, red balls and black balls are either paired with each other or can fill single slots on the table. Also red balls cannot be horizontally or vertically adjacent to other red balls, and black balls not adjacent to other black balls

The numbers at the side and bottom of the grid give (only) some of the numbers of red or black balls in the respective columns or rows.

dipoles.bmp

Any questions for clarifications, please on here, answers by PM. Have fun!

[snookersfun]

newsbreak: abextra solved R.395 already. Very well done!

the nice picture solutions for R.394 can come up on the thread now as well.

[Monique]

R394 ... colour paths
R394ways2F.bmp

[snookersfun]

Mon, thanks for the beautiful art of touching balls of standard size

congratulations again to all the solvers of R.394, moglet, Mon, abextra and d_g!

and update R. 395: Mon solved that as well now. Congratulations!

[snookersfun]

update: R.395 solved by moglet yesterday. Congratulations!

and R. 396: Balls in order

In the following diagram, please arrange 9 each of the 9 coloured balls of Snooker Plus on the 9x9 part of the table. Every ball appears once in every column, row, and outlined 3x3 area. Moreover the balls should be arranged in the order shown (just not necessarily directly neighbouring) for those rows and columns which have an ordered line of balls preceding them.
colours-2.bmp
answers by PM please

[crucible77]

update: R.395 solved by moglet yesterday. Congratulations!

and R. 396: Balls in order

In the following diagram, please arrange 9 each of the 9 coloured balls of Snooker Plus on the 9x9 part of the table. Every ball appears once in every column, row, and outlined 3x3 area. Moreover the balls should be arranged in the order shown (just not necessarily directly neighbouring) for those rows and columns which have an ordered line of balls preceding them.
[ATTACH]2186[/ATTACH]
answers by PM please

its sunday!

[snookersfun]

oops, blunder!!

I forgot to give you one starting ball. I hope I haven't had people working too hard on it

Corrected now on the original post.

[snookersfun]

...and moglet in first on the Sudoko Snooker Plus. Congratulations

[snookersfun]

...and moglet in first on the Sudoko Snooker Plus. Congratulations

...and though I was lazy updating, Mon and abextra are there as well now. Congratulations!!!

[snookersfun]

I think we can close the sudoko/snooker plus round. Does anybody want to put up his colourful solution?

and for the weekend:
R.397 snooker trading

Oliver and Charlie headed off to Barry the Baboon's shop to trade some of their excess sets of collectively owned snooker balls. It finally turned out that the amount of money they received for each set is the same as the number of sets sold to Barry.

The two apes decided to buy a large supply of triangle chalk for the money just earned and got a good price at 10 GPB for a pack (24 pieces each). They bought as many packs of triangle chalk as they could and for the money left threw in a cue towel.

On their way home they decided to split up the goods, but noticed that there was one package of triangle chalk left over. Not wanting to open it up, Oliver offered, 'I'll take the carton of chalks and you take that cue towel'. But Charlie was not happy with that: 'That towel costs less than the chalks, so is not fair'. 'Alright' concurred Oliver, 'I will give you one of my tip clamps in addition, and we are even.'

What is the value of the tip clamp?

Answer by PM please

[moglet]

R396

This was my solution:

[snookersfun]

thank you moglet, very nice picture

and update to R. 397: this was first solved perfectly by d_g (thought I just mention it, as the previous rounds seem to take him forever), followed by moglet, and abextra and Mon need to make some small adjustments but are basically there as well.

So with that we can tighten that clamp a bit and:

R. 398: filling boxes

Coming back home the apes meet up with Gordon and Gwenny and look over their boxes of spare balls. Balls are generally boxed by colours and each box can contain up to 30 balls.
Gordon, Charlie and Oliver each take an open box already containing some green, blue and pink balls respectively (all different numbers) and then take turns adding one ball each of their particular colour fished out from the 'messy box' (a huge box where leftover balls are often initially thrown in regardless of colour for later sorting) into their boxes.

Gwenny, running around between them and peeping into all the boxes suddenly pipes up:
Oh, this is interesting; on this round of turns the amount of pink balls Oliver has accumulated in his box sums up to the sum of the digits of the amount of blue added to the sum of the digits of the amount of green balls Charlie and Gordon have amassed.
Furthermore, on the round before one could have observed the same for the amount of Gordon's balls (then being the sum of the digits of the two other ape's balls) and in 6 more rounds, finally Charlie's sum will equal the sum of the digits of the other two balls.

So, how many balls did each ape have when Gwenny made the observation?

answers and explanations by PM please