Puzzles with numbers and things

[abextra]

Round 146 Ape Break Bonanza

Ape Break Bonanza is like normal snooker, with 15 reds, but now there are 4 extra colours...
As ever, your question is: what is the highest break (ignoring free balls) you can make?

You don't need to say the highest theoretically possible - you just need to bid the highest break that YOU can find.


....

I'll go for 263.

EDIT : Oops, I forgot the red balls! I bid 278.

[davis_greatest]

Like this:

OOOO
OOOO
OOOO
OOOO

Two horizontal, two verticl and two diagonal rows, each of four coins!

That looks perfectly good to me! ... although I must confess, it was not the answer I was expecting.

Both snookersfun and abextra came up with my answer, which was.... a clue: think "STAR"

... and this now makes me wonder, how many other possible ways might there be of doing this? (I don't know the answer to that question!)

[The Statman]

Like this:

OOOO
OOOO
OOOO
OOOO

Two horizontal, two verticl and two diagonal rows, each of four coins!

[davis_greatest]

First, a reminder that round 145 is still open....

Round 145 - Malta Cup bonanza

Stephen Hendry has just defeated seven-time and defending World Champion Steve Davis in the Final of the 2008 Malta Cup, after the Nugget had to retire from the match due to concussion induced by being jostled by fans against a doorframe, and Hendry has pocketed the 12p first prize.

Hendry lays the twelve pennies out on the snooker table in pride, and arranges them in six lines of four coins each. How does he do this?

------------------------------------------------------------------------------

And second, for those who found round 144 with six colours and six pockets too easy, here is the same puzzle but with ten colours and ten pockets. Again, you score a bonus of three points if you pot a ball into a pocket the same colour as the ball, and you need to find the highest break possible.

Here is a full explanation of the game, in case you are not familiar by now...

Round 146 Ape Break Bonanza

Ape Break Bonanza is like normal snooker, with 15 reds, but now there are 4 extra colours. You have to pot red, colour, red, colour etc, just like in normal snooker, but then pot the 10 colours in order (instead of the usual six).

The colours are:

yellow: 2 points (that says yellow: 2 points)
green: 3 points
brown: 4 points
blue: 5 points
pink: 6 points
black: 7 points
orange: 8 points
silver: 9 points
olive: 10 points
purple: 11 points


There are 10 pockets (one extra pocket added on each edge of the table). From top left, going clockwise, the pockets are:

purple, brown, orange, green, pink, silver, blue, olive, yellow, black

So the table looks a bit like this, with the value of the colour of each pocket shown for those who may be colour blind.

11------4------8
!......................!
!......................!
!......................!
7.....................3
!......................!
!......................!
!......................!
2.....................6
!......................!
!......................!
!......................!
10------5------9


The rules are:

a) Once a colour has been potted, the same colour cannot be potted following the next red, nor following the red after that. (Once the 15th red and colour have been potted, this rule no longer applies - the final colours may and must be potted in the usual order of yellow, green, brown, blue, pink, black, orange, silver, olive, purple, regardless of the colours potted with the final reds.)

Example 1: Red Brown Red Yellow Red Blue Red Brown IS allowed
BUT
Example 2: Red Brown Red Yellow Red Brown IS NOT

Example 3: For the 14th and 15th reds,
Red Black Red Yellow Yellow Green Brown Blue Pink Black Orange Silver Olive Purple IS allowed



b) Whenever a colour has been potted, the following colour cannot be potted into any pocket that lies along the same edge of the table. That means that, if the pocket is on the side cushion, the next colour cannot be potted into a pocket on the same side of the table (left or right); and, if the pocket is on an end cushion, the next colour cannot be potted into a pocket at the same end of the table either. Corner pockets, of course, lie on side and end cushions!

This applies even when down to the final 10 colours.

For example, after potting a colour into the orange pocket, it would not be permissible to pot the next colour into the orange, green, pink or silver pockets (same side), nor into the purple or brown pockets (same end). As a second example, after potting a colour into the brown pocket, it would not be permissible to pot the next colour into the brown, orange or purple pockets (same end).


c) None of these rules apply to reds. It makes no difference into which pockets reds are potted.

d) And this is the important bit: potting a colour into a pocket of the same colour as the ball scores a bonus of 3 points (so potting pink into pink pocket would score 6+3 = 9 points).


As ever, your question is: what is the highest break (ignoring free balls) you can make?

You don't need to say the highest theoretically possible - you just need to bid the highest break that YOU can find.

If your bid is highest, you will be asked to explain how you get your break. For example, you might say:

Red
Green into Yellow pocket (or whatever)
Red
Pink into Orange pocket (or whatever)
....
...

and after all 15 reds and colours...

Yellow into Yellow pocket (or whatever)
Green into Silver pocket (or whatever)
Brown into Black pocket (or whatever)
....

[davis_greatest]

Hi everyone my 163 is here. I thought it was impossible for most of the time I was looking for it.

Well done, dan! So, you didn't believe me?

Yes, the trick is...not to try to pot every colour into a pocket of the same colour. You need to pot one black into a different colour pocket!

[dantuck_7]

B P S 12
1 6 6 10 10
2 5 5 9 19
3 3 3 7 26
4 7 2 8 34 KEY HERE
5 6 6 10 44
6 5 5 9 53
7 3 3 7 60
8 7 7 11 71
9 4 4 8 79
10 2 2 6 85
11 6 6 10 95
12 5 5 9 104
13 3 3 7 111
14 7 7 11 122
15 4 4 8 130
Y 2 2 5 135
G 3 3 6 141
B 4 5 4 145
B 5 3 5 150
P 6 7 6 156
B 7 4 7 163

Hi everyone my 163 is here. I thought it was impossible for most of the time I was looking for it.

[davis_greatest]

The 163 you just sent me looks good, dan! (There are variations on the same theme that will also give 163.) Post it on this thread!

(Um... not really sure how I thought of it - I was just standing on a crowded train and it came to me, I suppose...)

[dantuck_7]

Yep let everyone know the solution. How did you think up this puzzle? Was my 163 okay.

[davis_greatest]

Yep - please let everyone know ( I have even been told the format of the break and still can't get it!!).

Shall we say 12 AM GMT.

Dan.

P.S - How did you dream this up davis?
P.P.S - Think I've got it now! Phew!

Sorry - let everyone know what?
How did I dream up what?

[dantuck_7]

Yep - please let everyone know ( I have even been told the format of the break and still can't get it!!).

Shall we say 12 AM GMT.

Dan.

P.S - How did you dream this up davis?
P.P.S - Think I've got it now! Phew!

[davis_greatest]

Quick update on this... I've had good answers to round 145 from snookersfun and abextra (including a very original one first from abextra, which I wasn't expecting). Any other offers?

I've also had a claimed 163 break sent to me for round 144. I'm not quite sure what to make of it though, since it seemed to involve an "8-ball" being potted in the first shot. Edit - this bid has now been retracted. I know that a few people have spent a lot of time trying to get the 163 break - so if still no success, I may put it up on this thread tonight or tomorrow.

Don't forget that round 144 is still open!

But here, for those who like money, is ....

Round 145 - Malta Cup bonanza

Stephen Hendry has just defeated seven-time and defending World Champion Steve Davis in the Final of the 2008 Malta Cup, after the Nugget had to retire from the match due to concussion induced by being jostled by fans against a doorframe, and Hendry has pocketed the 12p first prize.

Hendry lays the twelve pennies out on the snooker table in pride, and arranges them in six lines of four coins each. How does he do this?

(PS I am terrible at solving this kind of question, so am bound to be even worse at trying to make one up - I therefore apologise if this proves laughably easy.)

[davis_greatest]

Here is dantuck's (computer's) break of 161, sent to me by pager:

...B P
1 6 6
2 5 5
3 3 3
4 7 7
5 4 4
6 2 2
7 6 6
8 5 5
9 3 3
10 2 2
11 6 6
12 5 5
13 3 3
14 7 7
15 4 4
Y 2 2
G 3 3
B 4 5
B 5 3
P 6 7
B 7 3

I haven't checked it, but will take your word for it,.... and yes, dantuck, I am sure that 163 is possible!

[davis_greatest]

OK, here's my 162

With red balls

black into black (7+3), green into green (3+3), blue into blue (5+3), pink into green (6)
black into black (7+3), green into green (3+3), blue into blue (5+3), pink into green (6)
black into black (7+3), green into green (3+3), blue into blue (5+3), pink into green (6)
black into black (7+3), green into green (3+3), blue into blue (5+3)

15 + 40 + 24 + 32 + 18 = 129 points

yellow into green (2), green into yellow (3), brown into brown (4+3), blue into yellow (5),
pink into pink (6+3), black into blue (7)

2 + 3 + 7 + 5 + 9 + 7 = 33 points

in total 129 + 33 = 162 points

Another very nice 162, abextra!

[dantuck_7]

Am onto the 163 - will send you a PM in a bit.

[abextra]

OK, here's my 162

With red balls

black into black (7+3), green into green (3+3), blue into blue (5+3), pink into green (6)
black into black (7+3), green into green (3+3), blue into blue (5+3), pink into green (6)
black into black (7+3), green into green (3+3), blue into blue (5+3), pink into green (6)
black into black (7+3), green into green (3+3), blue into blue (5+3)

15 + 40 + 24 + 32 + 18 = 129 points

yellow into green (2), green into yellow (3), brown into brown (4+3), blue into yellow (5),
pink into pink (6+3), black into blue (7)

2 + 3 + 7 + 5 + 9 + 7 = 33 points

in total 129 + 33 = 162 points