Puzzles with numbers and things

[davis_greatest]

Round 58 Big Ape Break scoring - Congratulations snookersfun and Vidas!

Although I set the deadline for this round as this coming Friday evening, which hasn't yet arrived, I am now satisfied that Vidas's bid of 194 below cannot be beaten. I finally got round to making my computer calculate the optimal solution and it came up with the same solution as Vidas (alternatively you can pot the final yellow in the brown pocket, but that makes no difference). The computer showed that 194 is the highest break possible.

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.

So I am awarding the points now. In accordance with the rules,

1 point to snookersfun for bid of 192
1 point to Vidas for bid of 194
2nd point to Vidas for having the highest bid


SO HERE IS THE SCOREBOARD AFTER ROUND 59 BUT BEFORE SNOOKERSFUN'S ROUND 60* AND BEFORE ROUND 61 (TRIANGLE MAD)

snookersfun……………………….…..24
Vidas……………………………………….12½
abextra……………………………..…...11
davis_greatest…………………..……9½
robert602…………………………………6
elvaago...............................5
The Statman……………………..……3
Semih_Sayginer.....................2½

(some rounds may be worth more than one point)
(especially ones won by davis_greatest)

* snookersfun has set a deadline of 12 noon today, which is about 97 minutes away

[davis_greatest]

or I counted some twice (hopefully not)
I could try to prepare a list (numbering all the pieces of the puzzle)
didn't do more counting, due to trivial stuff like cooking, dinner etc.

Actually, I just noticed I had missed two. So I suspect that 66 is the answer. Could probably write a computer program to look for them all, but I don't have the patience

[snookersfun]

Looks like you are up to 66. I had a look earlier and counted up to 64. (I looked them by looking at whether each of the outside edges of the rectangle were used or not used, rather than counting the triangles as doubles, triples etc)

So I must have missed 2. Found any more yet?

or I counted some twice (hopefully not)
I could try to prepare a list (numbering all the pieces of the puzzle)
didn't do more counting, due to trivial stuff like cooking, dinner etc.

[davis_greatest]

so far I counted
14 single
16 doubles
10 tripples
8 made of 4
8 made of 5
and 4 made of 8
+ 2 of 10
+ 4 of 6 (just noticed those)
sure there are more...

Looks like you are up to 66. I had a look earlier and counted up to 64. (I looked them by looking at whether each of the outside edges of the rectangle were used or not used, rather than counting the triangles as doubles, triples etc)

So I must have missed 2. Found any more yet?

[snookersfun]

so far I counted
14 single
16 doubles
10 tripples
8 made of 4
8 made of 5
and 4 made of 8
+ 2 of 10
+ 4 of 6 (just noticed those)
sure there are more...

[davis_greatest]

Is that 40??

If you say so! I haven't got the foggiest idea

[Snooker Rocks!]

Is that 40??

[davis_greatest]

Wow!

......

[snookersfun]

here is the picture

[davis_greatest]

Round 61 - Triangle Mad

I will ask another question while round 58 and snookersfun's round 60 are still alive.

Round 61....

I'm not sure whether I will award any points for this though - hopefully I will - the problem is I'm not sure I'll get it right so I might not know if you have! So it might have to be just for fun unless I am confident of the answer, which I haven't tried to work out yet.

Anyway, here it is...

Gordon is playing on his snooker table. The centres of the three pockets on the left hand side of the table are all in straight line, and similarly for the centres of the three pockets on the right hand side. He then draws straight lines with chalk connecting the centres of each pair of pockets.

The Statman, if you are reading this, perhaps you would care to grace us with a picture? I couldn't attempt it.

How many triangles are formed by these lines?


PS You can post answers to this on the thread, instead of by Private Message.

[snookersfun]

May I take the opportunity to remind everybody interested in points of the fast approaching deadline of my last puzzle (less than 21 hours). I only have one customer so far. If d_g solved it, so can you!

So, here is the next round. According to the new rules, I shall have the answers PMed as well. Deadline is until Wednesday 12:00 pm (d_g's time).

Assume that there is a big sack with an equal number each of several colored snooker balls (there might be more than the traditional 6 colors though- I am just madly trying to relate this thing to snooker). Now, if one adds 20 balls of a new color to this mix, one wouldn't change the probability of picking two balls of the same color from the bag. (This is w.o. returning the balls after the picks).
The question is how many balls were in the sack, before those balls were added?

[davis_greatest]

Updated scoreboard

have my half then. I am just happy, I finally understood what I was doing!

No trading / donating points! They are too important

The last scoreboard seemed pages and pages back - hopefully I have found the right one and not removed any points from anyone...

HERE IS THE SCOREBOARD AFTER ROUND 59 BUT BEFORE ROUND 58* AND BEFORE ROUND 60**

snookersfun……………………….…..23
abextra……………………………..…...11
Vidas……………………………………….10½
davis_greatest…………………..……9½
robert602…………………………………6
elvaago...............................5
The Statman……………………..……3
Semih_Sayginer.....................2½

(some rounds may be worth more than one point)
(especially ones won by davis_greatest)

* Round 58, Big Ape Break, is still open with a deadline of this Friday at 23:00 GMT. At the moment, snookersfun and Vidas have a point each (provisional on no one finding any errors) and, if no one improves on Vidas's bid of 194, Vidas will get an additional point. None of those points have been shown in the scoreboard above.

** Round 60 has been asked by snookersfun. snookersfun, has anyone else answered it yet?

[elvaago]

Oh, I missed the part where I got half a point.

I'll accept this!

[snookersfun]

I completely impartially submit the notion I should get a point for this. :-)

have my half then. I am just happy, I finally understood what I was doing!

[davis_greatest]

I completely impartially submit the notion I should get a point for this. :-)

Hehe - nice try How about another variation on a theme to come up with the answer.... this one is based on imagining first that Oliver (rather than Charlie) were to have the first shot.

Prob(Oliver wins if Oliver starts)

= Prob(Oliver pots) + Prob(Oliver misses) . Prob(Charlie misses).Prob(Oliver wins if Oliver starts)

= 1/3 + 2/3 x 1/3 x Prob(Oliver wins if Oliver starts)
= 1/3 + 2/9 x Prob(Oliver wins if Oliver starts)

So 7/9 x Prob(Oliver wins if Oliver starts)= 1/3

So Prob(Oliver wins if Oliver starts)= (1/3) / (7/9) = 3/7

But, in the question, Charlie starts, not Oliver.

Prob(Oliver wins if Charlie starts) = Prob(Charlie misses) x Prob(Oliver wins if Oliver starts)

= 1/3 x 3/7 = 1/7

as before! I'll stop there