Puzzles with numbers and things

[davis_greatest]

Well let me try ...

The total number of points distributed in one league is between 135 (3*45) and 90 (2*45) as there are 45 matches and 3 points are distributed when there is a winner and 2 when there is a draw.
The winner of the league must ncessarily have strictly more points than the average number of point per player (strict equality is not acceptable) meaning a minimum of 10 points. This can't be done without winning at least one match because all draws - that would then be the best possible result - yields only 9.

Yes, almost there. However, there is still a little gap in the proof as you need to explain why the part I have highlighted in red. The fact that two apes finish on the same number of points does not, on its own, mean that one can't be placed above the other. (Remember, if points are the same, we then compare frame difference and then at results among matches involving the tied apes.)

(If everyone finishes the same, no one is top.)

This means same points, same frame difference, same results among tied apes... not just same total points.

[Monique]

Well if average is >9 then it implies at least one win anyway. So the only case we have to consider is average is 9. This means all matches were draws. So there is no frame difference and tied apes drawed. Strict equality. That's why I brough up the question about score frames to start with ...

[davis_greatest]

Yes, indeed! No gaps left.... and congratulations again Monique

[davis_greatest]

Round 309 - Charlie in his prime

Charlie has just made a Prime Maximum Break.

A Prime Maximum Break in snooker is the maximum break that one can (theoretically) get that is also a prime number - not only that, but to qualify, the running break after every shot must also be a prime number.

What was Charlie's break?

Answers on the thread please...

[Monique]

First bid : 37 ...

[dantuck_7]

2nd bid 47.

I was going to set my PC to have a search but I'm too tired to sort it out!

[snookersfun]

47 sounds alright

[davis_greatest]

Yes, 47 is the Prime Maximum Break! Please explain a way to get it...

[snookersfun]

Starting with a free ball
Free ball + red-2
Green-5
2 reds-7
brown-11
2 reds-13
pink-19
4 reds-23
pink-29
2 reds-31
pink-37
4 reds-41
pink-47

[davis_greatest]

Starting with a free ball
Free ball + red-2
Green-5
2 reds-7
brown-11
2 reds-13
pink-19
4 reds-23
pink-29
2 reds-31
pink-37
4 reds-41
pink-47

Congratulations. dantuck, did you have the same?

Monique, what was your 37? The same up to the 37 above but without using a free ball?

[Monique]

yes, that was my first attempt last night ...

then came to
red-1
Brown-5
2 reds-7
brown-11
2 reds-13
pink-19
4 reds-23
pink-29
2 reds-31
pink-37
4 reds-41
pink-47
this morning when stuck (as a passenger) in traffic jams ...
with no need for a free ball (but considereing 1 as a prime)
though about the free ball possibility and whether this could lead us further but didn't find one. Envisaged also scenarios starting from a colour as was discussed recently (the maximum discussion) ...
too late anyway!

[davis_greatest]

Round 310 Maximum Mayhem

I just refereed a frame between my pet chimpanzee Charlie and pet gorilla Gordon.

When Gordon came to the table for his final visit, the reds were scattered everywhere, and he had a clear view to both extreme edges of at least 7 reds, including one hanging over a corner pocket. He went on to make a tremendous break, potting a black after each of the 15 reds, and then the first 5 colours. He slammed the final black in, and after the black had dropped, the white flew around the table off 7 cushions. However, as the cue ball was slowing right down, it became obvious that its path would send it dropping into the corner pocket.

Gordon picked the white up, while it was still moving, before it could reach the pocket. However, by then, I had already called, quite a few seconds earlier, "One hundred and forty seven!"

The 147 break still stood, and I had made no errors in my refereeing. Why?

Again, answers on the thread please.

[davis_greatest]

Sorry - if anyone has already read the above post in the last 2 minutes, I just edited the wording a little...

[Monique]

Because He was on a 154 starting with a black ... scenarios to be found in the "maximum" discussion thread?

[davis_greatest]

Because He was on a 154 starting with a black ... scenarios to be found in the "maximum" discussion thread?

Yes! Congratulations, Monique - and very quick! Exactly so. He had been put back in by Charlie after a "Foul and a Miss", having missed a colour following a "free ball" red on his previous visit.