Puzzles with numbers and things

[davis_greatest]

Another round 305 update - a couple of other answers have come in (much earlier today). The one from abextra was correct - congratulations

Next person to answer, please do so on thread. This one really isn't that hard...

[Monique]

So I think Gordon can win 4-0 ...

If Quinten plays each frame like this: pots 15 reds without colours, then yellow and green: 17 balls , 20 points: then Gordon pots remaining colors : 4 balls 22 points.

Gordon wins 4 frames potting only 16 balls.

[davis_greatest]

So I think Gordon can win 4-0 ...

If Quinten plays each frame like this: pots 15 reds without colours, then yellow and green: 17 balls , 20 points: then Gordon pots remaining colors : 4 balls 22 points.

Gordon wins 4 frames potting only 16 balls.

Yes! Congratulations Monique, abextra and snookersfun! Gordon can still whitewash his naughty new friend!

PS There is no need, of course, for Quinten to pot any more than one ball each visit.

[davis_greatest]

Round 306 - The Great Ape Maltese Open

At the Great Ape Maltese Open, 640 apes take part. They are divided into 64 round robin groups of 10; and in each group, each ape plays each of the other 9 apes. The winner of each group qualifies for the knock-out stage (only one ape qualifies per group).

Each round robin match consists of 6 frames (all frames are played, so it could finish 3-3 or 6-0, say). Apes get 3 points for a win and 1 for a draw.

The ape with the most points in each group qualifies. If points are the same, they look at frame difference. If that is the same, they look at results among matches involving the tied apes.

By some freak of timetabling, Oliver is scheduled to play all 9 of his group matches before the other matches in his group have been played.

How many of his opening matches can he afford to lose 4-2 and still have his chance of winning the tournament lying solely in his hands?

("Lying solely in his hands" means that he does not have to rely in any way on results of matches in which he is not playing.)

Answer on the thread please.

[Monique]

I'd say none ...
If he looses one, his opponent in that match still may win all his matches and then be qualified or in any case be above him in results table.
Or do I misunderstand something?

[R_Demarco]

I like to add one little easy puzzle. . (cramped for time to solve any at this moment )

once, neat, rent, town, either, vent, axis, flour.

Find the logic and the word hidden in the above list?

[snookersfun]

R_D's:

the word is (followed in hidden text-select to read): carnival

[davis_greatest]

I'd say none ...
If he looses one, his opponent in that match still may win all his matches and then be qualified or in any case be above him in results table.
Or do I misunderstand something?

No, you don't misunderstand!

That is, of course, correct. Congratulations If you lose a single match in a league / round robin group, no matter how large, then you can't be sure of finishing at the top of the league even if you win every other match.

[davis_greatest]

Round 306 - The Great Ape Maltese Open

At the Great Ape Maltese Open, 640 apes take part. They are divided into 64 round robin groups of 10; and in each group, each ape plays each of the other 9 apes. The winner of each group qualifies for the knock-out stage (only one ape qualifies per group).

Each round robin match consists of 6 frames (all frames are played, so it could finish 3-3 or 6-0, say). Apes get 3 points for a win and 1 for a draw.

The ape with the most points in each group qualifies. If points are the same, they look at frame difference. If that is the same, they look at results among matches involving the tied apes.

By some freak of timetabling, Oliver is scheduled to play all 9 of his group matches before the other matches in his group have been played.

How many of his opening matches can he afford to lose 4-2 and still have his chance of winning the tournament lying solely in his hands?

("Lying solely in his hands" means that he does not have to rely in any way on results of matches in which he is not playing.)

Answer on the thread please.

Round 308 - Good old Gordon!

Fortunately, Gordon (in a different group from Oliver) finished top of his group in the Great Ape Maltese Open.

What is the minimum number of matches that he must have won?

[Monique]

what if, all previous factors being the same "tied apes" had a draw? Look at scores?

If yes I'd say he need no victory ... in a very unlikely scenario but theoretically possible.

[davis_greatest]

what if, all previous factors being the same "tied apes" had a draw? Look at scores?

If yes I'd say he need no victory ... in a very unlikely scenario but theoretically possible.

Can you give an example of how he could finish top with no victories?

Edit: PS what do you mean by look at scores? Match scores (number of frames), yes - points scores within frames, no.

[Monique]

What I had in mind ...

if all matches in his group end up as draws and Gordon only looses frames by the smallest possible difference while he wins frames systematically 147-0 ...

but with your additional info it does not qualify.

Otherwise one win is certainly sufficient if all other matches in that league end up as draws.

[davis_greatest]

What I had in mind ...

if all matches in his group end up as draws and Gordon only looses frames by the smallest possible difference while he wins frames systematically 147-0 ...

but with your additional info it does not qualify.

Otherwise one win is certainly sufficient if all other matches in that league end up as draws.

Yes... so we know now that with 1 win it is possible to finish top of the group.

So just need to prove that it is not possible to finish top with zero wins - can you (or anyone else) give this proof?

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

[R_Demarco]

Correct! Toll! Too easy, I suppose!

Anyone else? Plus explanation, please.

R_D's:

the word is (followed in hidden text-select to read):

[Monique]

R305

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.