Puzzles with numbers and things

[davis_greatest]

PM me your details d_g and ill wire ya a quid for every point you give me for my, ahem, "answers" by PM.

HERE IS THE SCOREBOARD ...

...
...
Semih_Sayginer.....................2½

I'm still waiting for that £2.50

[elvaago]

Let me type out my solution, can you tell me where I went wrong?
Let's say Charlie potting is CP, charlie missing is CM, Oliver potting is OP and Oliver missing is OM.

CP = 2 OP
CP = OM
CM = OP

OM + OP = 1
2OM + 2OP = 2
2OM + CP = 2
2CP + CP = 2
3CP = 2
CP = 2/3
CM = OP = CP/2 = 1/3

OK I see where I went wrong originally.
For Oliver to win, Charlie needs to miss and then Oliver needs to pot. 1/3 * 1/3 = 1/9. That's my final answer and if it's wrong, someone else can get it. ;-)

[davis_greatest]

Round 59 update

Bid of 192 - 1 point for snookersfun
Bid of 194 - 1 point for Vidas

Highest bid to date is 194, by Vidas. If this remains the highest at the Deadline of 23:00 GMT on 24 November, Vidas would score a 2nd point.

All points so far are provisional on no errors being found in the solutions - if anyone thinks that either snookersfun's or Vidas's solutions contain an error, please raise it on this thread, stating where the error is.

Any advance on 194?

[Semih_Sayginer]

PM me your details d_g and ill wire ya a quid for every point you give me for my, ahem, "answers" by PM.

[elvaago]

Yes, I said 1/16th first but I changed it like, 20 seconds later. I'll have to recheck my calculations. :-)

[davis_greatest]

Is it 1/36th?

Didn't you say 1/16 first? No editing of answers please - it makes it very difficult for me to score them!

It is not 1/16, nor 1/36!

[davis_greatest]

Important Announcement - New Rules For Answering Questions

We are going to try out some new rules for answering questions on this thread. They will apply from round 60 onwards only (not yet posted) and apply for a trial run while I see how they are working, until further notice.

All rounds already asked (rounds 58 and 59) are unaffected.

The new rule is intended to give people more time to answer the questions. Especially, I am concerned that snookersfun is not getting in quickly enough with her answers and is therefore struggling badly on the leaderboard, so this should give her more time. It is also to help people who cannot read the questions until certain times of day, so they may not currently always have a chance to answer.

New rule: each question (unless stated otherwise) will have an Initial Deadline, stated in the question (probably typically 48 or 72 hours, but may vary depending on difficulty and my mood). Within that Initial Deadline, anyone answering the question is requested to do so only by Private Message to me, rather than posting the answer on the thread.

Then, everyone who answers correctly within that initial deadline will score a point and there may be an additional point for the first to answer (at my discretion).

At the end of the Initial Deadline, I will invite answers to be posted on the thread, or I may paste them from the private messages. I will also give my suggested solution, as usual.

If you have any queries on the questions, requiring clarification, then of course post them on the thread as normal.

I may extend the Initial Deadline at any time, and if so, will say so on the thread.

This is just a trial, to see how it goes...

[elvaago]

Is it 1/36th?

Charlie and Oliver are playing Big Ape Break, and are level on points... it has gone to a respotted black - they have each had a few shots, but no one has potted it yet.

Charlie always has the same chance of potting the black with every shot he plays, no matter what the position of the balls - and the same goes for Oliver; but, at each attempt, Charlie is twice as likely to pot it as Oliver is.

Also, with each attempt, Charlie is as likely to pot the black as Oliver is to miss it and, of course, Oliver is as likely to pot the black as Charlie is to miss it. Neither ape will ever foul.

Charlie is about to take the next shot. What are Oliver's chances of winning the frame?



Note: Round 58 is of course still open until 23:00 GMT on Friday 24 November, but we'll carry on with other rounds in the meantime.

[snookersfun]

I just did, as to how I remember the placing of the colours, it looks astonishingly good.

[davis_greatest]

Ok, here is what I could find for now (check valid or not.)

1)black-14 (black pocket)
2)green-6 (green pocket)
3)blue-10 (blue pocket)
4)pink-6 (green pocket)
5)black-14 (black pocket)
6)green-6 (green pocket)
7)blue-10 (blue pocket)
8)pink-6 (green pocket)
9)black-14 (black pocket)
10)green-6 (green pocket)
11)blue-10 (blue pocket)
12)pink-12 (pink pocket)
13)yellow-4 (yellow pocket)
14)brown-8 (brown)
15)black-14 (black)
===============
140 points +15 reds = 155 pts
final colours
yellow -2 (green pocket)
green -3 (yellow pocket)
brown -4 (green pocket)
blue -10 (blue pocket)
pink -6 (green pocket)
black -14 (black pocket)
==========================
39 pts
Total: 194.

I haven't checked this in detail but from my first look, I can't see anything wrong with this. Does anyone else want to check it?

Perhaps snookersfun will check it thoroughly?.... as this is taking the new lead!

[Vidas]

Ok, here is what I could find for now (check valid or not.)

1)black-14 (black pocket)
2)green-6 (green pocket)
3)blue-10 (blue pocket)
4)pink-6 (green pocket)
5)black-14 (black pocket)
6)green-6 (green pocket)
7)blue-10 (blue pocket)
8)pink-6 (green pocket)
9)black-14 (black pocket)
10)green-6 (green pocket)
11)blue-10 (blue pocket)
12)pink-12 (pink pocket)
13)yellow-4 (yellow pocket)
14)brown-8 (brown)
15)black-14 (black)
===============
140 points +15 reds = 155 pts
final colours
yellow -2 (green pocket)
green -3 (yellow pocket)
brown -4 (green pocket)
blue -10 (blue pocket)
pink -6 (green pocket)
black -14 (black pocket)
==========================
39 pts
Total: 194.

[davis_greatest]

Round 59 - Respotted Banana

Charlie and Oliver are playing Big Ape Break, and are level on points... it has gone to a respotted black - they have each had a few shots, but no one has potted it yet.

Charlie always has the same chance of potting the black with every shot he plays, no matter what the position of the balls - and the same goes for Oliver; but, at each attempt, Charlie is twice as likely to pot it as Oliver is.

Also, with each attempt, Charlie is as likely to pot the black as Oliver is to miss it and, of course, Oliver is as likely to pot the black as Charlie is to miss it. Neither ape will ever foul.

Charlie is about to take the next shot. What are Oliver's chances of winning the frame?



Note: Round 58 is of course still open until 23:00 GMT on Friday 24 November, but we'll carry on with other rounds in the meantime.

[davis_greatest]

Great problem.
i think maximum is higher than 192, but below 200.. Let's wait for the results.

I'm not sure if I am going to have a go at this myself before the deadline... I still haven't tried it semi-seriously. Vidas, why don't you post something above 192 if you can find something...

Deadline is still 5 days away!

[Vidas]

Great problem.
i think maximum is higher than 192, but below 200.. Let's wait for the results.

[davis_greatest]

...I wanted to add 'while it lasts'
If you would do that, would you have the steps as well? Anyway, why don't you?

Yes, of course I would have the steps. It's just a case of finding the time. I'm a bit rusty so I think to figure out the optimal solution might take me the best part of an hour. Writing the program to pot balls randomly, according to the rules, was much quicker.