Puzzles with numbers and things

[elvaago]

I have no idea what the answer is to this one, but I figured it might be a fun question for the Big Brains to crack their heads over.

Round 104.

My dog Vlad likes to play snooker. He's not very talented, as you might expect from someone with no thumbs, but he's very enthusiastic. He enjoys playing with the white ball only. This is how he plays. He puts the white ball on the blue spot and then plays it into a random direction at high speed. This random direction is not in the direction of a pocket and it's also not at a 90 degree angle to any cushion. He also can only play the white ball at whole degrees. He then likes watching the white ball race around the table and if he happens to pot it, he gets a treat from me. It's really fun. You should try it some time.

Every time the white ball hits a cushion, it loses 1% of the speed it has at the time.

Ignoring physics that would no doubt make the white ball leave the table when played at such speeds, answer the following questions:

- What are the chances of the white ball being potted?
- How many cushions would you expect it to hit?
- What is the least amount of cushions it has to hit?
- What is the maximum amount of cushions it can hit?

Answers with explanations on this thread.

[Semih_Sayginer]

So here is the latest Puzzles with numbers and things Hall of FRame

i like it d_g

[davis_greatest]

Well - it looks like we have a new entrant to the Puzzles with numbers and things Hall of Fame! Welcome to the thread!

That is enough for the point....

Ooops - I just remembered that there are no points any more! I meant "that is enough for a place in the Hall of Fame" ...

[davis_greatest]

So here is the latest Puzzles with numbers and things Hall of Fame

Oliver (my pet orang-utan)
Gordon (my pet gorilla)
Charlie (my pet chimpanzee)
snookersfun
abextra
davis_greatest (Oliver's, Gordon's and Charlie's pet something)
Vidas
chasmmi
elvaago
robert602
Sarmu
The Statman
austrian_girl
austrian_girl's dad
Semih_Sayginer
Snooker Rocks!
Ginger_Freak
April Madness
steveb72

[davis_greatest]

Congratulations steveb72!

As long as I have understood the question.........

Yes, you potted the black ball for a total clearance of 105 and you potted it into the middle pocket on the yellow ball side of the table (if you know what I mean!).

From the 15 reds you potted 3 yellow, 3 greens, 3 browns, 2 blues, 2 pinks and two blacks taking your break to 78. You then potted all of the colours for a total clearance of 105.

In total you would have potted 4 yellows, 4 greens, 4 browns, 3 blues, 3 pinks and 3 blacks. Thus you have potted at least as many of the lower value colours (Yellow Green Brown) as the higher value colours (Blue Pink Black).

Well - it looks like we have a new entrant to the Puzzles with numbers and things Hall of Fame! Welcome to the thread!

That is enough for the point. In fact, while you cannot be sure that "from the 15 reds I potted 3 yellows, 3 greens, 3 browns, 2 blues, 2 pinks and two blacks" - since that is just one possibility - you can be sure that I did not reach the century until potting the final black. Since this must be the 36th ball, it must indeed be the centre pocket on the yellow side of the table (on my 6th go around the table).

The break you describe gives 105 and is the maximum possible break that satisfies the stated conditions. Since we know that I made a century, I must have scored somewhere in the range 100 to 105 - and therefore the final black must have been required for the century.

Another possibility would be, with the 15 reds, no blacks, and 3 each of yellow, green, brown, blue and pink. That would give a break of 102, which would still mean I had to pot the final black for the century - and hence would give the same answer.

[steveb72]

As long as I have understood the question.........

Yes, you potted the black ball for a total clearance of 105 and you potted it into the middle pocket on the yellow ball side of the table (if you know what I mean!).

From the 15 reds you potted 3 yellow, 3 greens, 3 browns, 2 blues, 2 pinks and two blacks taking your break to 78. You then potted all of the colours for a total clearance of 105.

In total you would have potted 4 yellows, 4 greens, 4 browns, 3 blues, 3 pinks and 3 blacks. Thus you have potted at least as many of the lower value colours (Yellow Green Brown) as the higher value colours (Blue Pink Black).

[davis_greatest]

Round 103 - Round we go!

Last night, I had the pleasure of making my first total clearance! Gordon broke off, sent a red right down the table into baulk, which I duly potted into the yellow pocket, and it all went from there! Funnily enough, it was also the first time that I had ever made a century, and when I potted the ball that gave me the century, Oliver and Charlie (who were watching intently) gave me whoops of excited applause.

Later, when thinking over the whole fantastic break in my mind (I am afraid that not only was I thinking over the break in my mind, which I usually find is the best place to think things over, except possibly for in my foot, but also the fantastic break was in my mind, rather than in reality), I noticed two curious things:

1) For any pair of different colours, I happened to have potted at least as many of the lower valued colour as the higher valued one. For example, I potted at least as many greens as blacks (green being lower valued than black), at least as many browns as pinks, etc.

2) Every pot I made was into a different pocket going clockwise round and round the table, moving along one pocket at a time!


So - is it possible to determine with certainty which ball I potted for the century and whoops of excited applause, and into which pocket? And if it is possible to determine this, which ball was it and into which pocket?

[snookersfun]

very nice Robert. Yes, I wondered myself, if that was clear enough. But the 2nd option wouldn't have led to anything...neither a third option, with only the tangent passing through that point
And you are in the Hall of fame already, so well done!

One more thing, how did you put these neat superscripts?

[Robert602]

does anybody need a hint for the circle question or just more time?

Because it's a nice break from circles under Möbius transformations

(x+1)² + (y-2)² = 10

Although I've got to say I wasn't sure from the way you worded it whether you meant the tangent line passes through the given point, or the tangent meets the circle at that point. I've assumed the latter as the former doesn't seem to give enough information.

Worked out by finding the bisector of the two given points, and the normal to the tangent, the intersection being the centre of the circle at (-1,2), then just plugging one of the points in to get the radius and complete the equation.

[snookersfun]

does anybody need a hint for the circle question or just more time?

[rambon]

Certainly the answer to the stated question ends in 2... because it is 6:01:32 which ends in 2 - I agree there. I was simply remarking that you could have Charlie only ever being hit at 02, 12, 22.... seconds but the expected time need not necessarily end in 2.

For example, suppose Barry had an 80% chance (instead of 20%) of hitting each egg, with nothing else changing. Then the chance that any given egg hits Charlie's face would be 80% x 50% = 40%.

So the expected number of eggs bowled until Charlie is hit is 100% / 40% = 2.5. This occurs at 17 seconds after 6pm!

I understand what you're saying 100%

[davis_greatest]

But you've added an "if" in there davis_greatest which moves the goalposts...

In the question has stated it had to end in 2

Certainly the answer to the stated question ends in 2... because it is 6:01:32 which ends in 2 - I agree there. I was simply remarking that you could have Charlie only ever being hit at 02, 12, 22.... seconds but the expected time need not necessarily end in 2.

For example, suppose Barry had an 80% chance (instead of 20%) of hitting each egg, with nothing else changing. Then the chance that any given egg hits Charlie's face would be 80% x 50% = 40%.

So the expected number of eggs bowled until Charlie is hit is 100% / 40% = 2.5. This occurs at 17 seconds after 6pm!

[rambon]

Incidentally, although the answer does end in 2 seconds, this does not have to be the case for the reason you gave. If, for instance, there had been a 50% chance that the game ended at 6:00:02 and a 50% chance that it ended at 6:00:12, then the expected time of ending would be halfway between, so 6:00:07, which does not end in 2

But you've added an "if" in there davis_greatest which moves the goalposts...

In the question has stated it had to end in 2

[snookersfun]

well, that was fun
a round of geometry (that's what I am learning with/for the kids constantly this year it seems) for the fame then:

Imagine a circle passing through the point (-4,1). Also a tangent (equation 3y-x=17) to the circle passes through the point (-2,5).

Question: What is the equation for this circle?

[davis_greatest]

And if he's English he probably will...

Hehe

The answer has to end in either 02, 12, 22, 32, 42, 52 seconds, as the throw is every 110 seconds, not ten seconds after the 2 seconds for the egg's journey have elapsed....

Can I have a point for that bit at least...?

Incidentally, although the answer does end in 2 seconds, this does not have to be the case for the reason you gave. If, for instance, there had been a 50% chance that the game ended at 6:00:02 and a 50% chance that it ended at 6:00:12, then the expected time of ending would be halfway between, so 6:00:07, which does not end in 2