Puzzles with numbers and things

[davis_greatest]

is a 193 possible (how many different ways) and how many ways of a 192 are there?

I don't know. My program doesn't list every possible way of potting the balls into different pockets - there are too many ways (trillions, I think) so it would take far too long to run if I tried to make it do that. All my program does is work out the maximum possible score and show one way (at least) that this could be achieved. It took me over an hour to write though, and takes perhaps 30 seconds to run. It came up with the same solution as Vidas.

The deadline is now over. I only really have the one serious attempt. (Elvaago gets an honorable mention for 'guessing' one factor right). Can I therefore ask d_g to put up his explanation and take another point.

Do you still have the PM I sent you with my answer? If so, can you send it back to me? ... I deleted it.

[davis_greatest]

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?

OK - solution as requested:

Let's say there are m colours; k balls of each colour.

So P[2 balls of same colour] = (k-1)/(mk-1)

After adding 20 balls of a (m+1)th colour:

P[2 balls of same colour] = [mk(k-1)+20.19]/[(mk+20)(mk+19)]

Equate the two probabilities:

Cancels to: m(21-2k) = 19, which is prime

We can't have m=1 (that would give k=1, so one ball, which doesn't satisfy the problem) so m=19, k=10

So 190 balls

[davis_greatest]

HERE IS THE SCOREBOARD AFTER ROUND 60 AND BEFORE ROUND 61 (TRIANGLE MAD)

snookersfun……………………….…..24
Vidas……………………………………….12½
abextra……………………………..…...11
davis_greatest…………………..……10½
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)


At the moment, it looks like the stiffest competition is around who will take the silver and bronze medals.

[austrian_girl]

Has round 61 been posted yet?

[snookersfun]

yes it has, welcome a_g
http://www.thesnookerforum.com/showp...count_830.html

[davis_greatest]

With a nice picture here, a_g:

http://www.thesnookerforum.com/showt...2-page_84.html

[davis_greatest]

Round 62 - Last Ball Loser

Gordon and Oliver are playing Last Ball Loser with some snooker balls. They start with a set of 15 red balls.

Gordon starts the first game. In a game, the ape starting takes 1, 2 or 3 of the balls (his choice how many) and rolls them into the pocket. Then it is the other ape's turn to roll 1, 2 or 3 balls into the pocket. They have alternate turns, continuing like this, and whoever takes the last ball(s) loses the game.

Then they play again - each game starting with one ball more than the previous game (so, they start with 16 balls for the 2nd game, then 17 for the 3rd etc). The winner of each game starts the following game.

The winner of the match is the first to win 10 games, and Gordon and Oliver both play as well as is possible.

Who wins the match and what is the final score?

[davis_greatest]

Oh yes - answers by Private Message please. Initial Deadline will be 16:00 GMT on Saturday 25 November. One point awarded to everyone who has sent me the correct answer by then.

[davis_greatest]

Round 63 - Bigger Ape Break

To compete with the success of the Saturday night snooker game show, Big Ape Break (from round 58), which was hosted by Gordon the gorilla, Charlie the chimpanzee is hosting his rival show, "Bigger Ape Break" on the other channel.

This show is exactly like Big Ape Break except for a minor difference - whenever a colour has been potted into a corner pocket, the following colour cannot be potted into a corner pocket but may be potted into either middle pocket. (The same rule as before applies to pots of a colour into the middle pocket - i.e. the next colour may not be potted into a pocket on the same side of the table.)

Here, for completeness, are the whole rules (the rest of which are just like Big Ape Break):


On the show, contestants play a frame of snooker, just like any normal frame of snooker except that:

a) each of the 6 pockets is coloured. The colours of the pockets are:
yellow for the left-centre pocket and then, moving clockwise, blue, brown, green, pink, black - a bit like this:

0------0
!.........!
!.........!
!.........!
0------0
!.........!
!.........!
!.........!
0------0

b) 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, 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 red,
Red Black Red Yellow Yellow Green Brown Blue Pink Black IS allowed


c) Whenever a colour has been potted into a middle pocket, the following colour cannot be potted into any pocket that lies along the same side (left or right) of the table. When a colour has been potted into a corner pocket, the following colour cannot be potted into a corner pocket.

This applies even when down to the final 6 colours.

For example:

* after potting a colour into the green pocket, it would not be permissible to pot the next colour into the green, brown or pink pockets;
* after potting a colour into the pink pocket, the next colour must be potted in the yellow or green pockets.

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

e) And this is the important bit: potting a colour into a pocket of the same colour as the ball (e.g. pink into pink pocket) scores double points (in this example 2 x 6 = 12).


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 send me the highest break that YOU can find by Private Message by the Initial Deadline of 18:00 GMT on Sunday 26 November.

2 points will be awarded for the highest break given, and 1 point to each person who submits another break that I like (I haven't worked out exactly what kind of breaks I'll like yet).

Depending on how the round goes, I may ask for breaks to be submitted on the thread, but not yet.

If you have any questions, please ask them on the thread.

You should explain how you get your break. For example, you might say:

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

and after all 15 reds and colours...

Yellow into Yellow pocket (or whatever)
Green into Pink pocket (or whatever)
Brown into Green pocket (or whatever)
....


Round 61 (Triangle Mad) and Round 62 (Last Ball Loser) are still open...

[davis_greatest]

Round 64 - Smaller Ape Break

And one more round, while on a roll... this is "Smaller Ape Break", hosted by Barry the Baboon.


Exactly the same rules as Bigger Ape Break, except potting a colour into a pocket the same colour as the ball scores a bonus of 2 points (NOT double points) - so, for example, potting the pink into the pink pocket scores 6 + bonus of 2 = 8 points.

And, exactly as before, what is the highest break (ignoring free balls) you can make?


Deadline for this one is 19:00 on Sunday 26 November...


PS Now I've written a program to solve these for me, I can ask a lot of similar ones very easily.

[davis_greatest]

Update to rounds 61, 62, 63 and 64

snookersfun has solved round 62 (Last Ball Loser), has found the best solution for round 63 (Bigger Ape Break), and has found a good but not the best possible solution for round 64 (Smaller Ape Break)!

Any other attempts? Remember, you have until the weekend, and anyone can score points - especially for a decent attempt to Bigger Ape Break or to Smaller Ape Break, even if your break is beaten


I will declare round 61 (Triangle Mad) closed in a day or two if there are no other attempts - snookersfun and I each found 66 triangles.

[hegeland]

Can I post a question?

ROUND 65

An frustrated snooker player (Statman ) throws away the brown ball after having missed an easy double into the left middle pocket. The ball lands on the floor between two tables 8.3552056 fathoms further away. The throw form an angle of 0.733038 radians with the horizontal plane. Assume the ball leaves his hand at 0.010439036 furlongs height. Ignore air resistance. Gravity about 9,82 m/s2.

With what initial velocity did Statman throw the ball? (meters/second)

[davis_greatest]

Round 64 update

I have now received by PM the best possible solution to Smaller Ape Break. But others can still get points too for submitting high breaks. If even snookersfun can do it, you can too!

[davis_greatest]

Can I post a question?

ROUND 65

An frustrated snooker player (Statman ) throws away the brown ball after having missed an easy double into the left middle pocket. The throw measures 8.3552056 fathoms. The throw form an angle of 0.733038 radians with the horizontal plane. Assume the ball leaves his hand at 0.010439036 furlongs height.

With what initial velocity did Statman throw the ball?

Do you want the answer posted here or sent to you by PM?

[davis_greatest]

And in what units would you like the answer? Inches per hour, or chains per lunar year?