Puzzles with numbers and things

[davis_greatest]

d_g, did you make this break with 7 balls only?

No, it is not possible with 7 balls.

[davis_greatest]

So I'll ask another...

Round 274 - Massive Mix-up

In my local Ape League, apes play each other whenever they like over matches as long as they like (sometimes marathon matches), and at the end of the match they call me for me to come and note down the score.

I like to give each ape a single Final Score for each match played. The Final Score is equal to the points that the ape scored in the final frame played, which I read off the scoreboard, plus 147 points for every previous frame won (because I never know how many points had been scored in previous frames), and I also give each ape a bonus 4 points just for playing the match.

For example, if an ape plays 3 frames and wins them all, scoring 100 points in the final frame, I give the ape 100 points (for final frame) + 294 points (2 x 147 points for winning the first 2 frames) + 4 points (for playing) = 398 Final Score.

Tonight, I just went to take down the score for Gordon's match against Oliver. I jotted down the number of frames won by each ape and the points score of the final frame. Then I went and calculated each ape's Final Score on my home computer.

Unfortunately, I mixed up the number of points that Gordon had got in the final frame with the number of frames he had previously won - i.e. I swapped them around, by mistake.

As a result, the Final Score I got for Gordon was the same as the Final Score I got for Oliver. If I had not made this mistake, Oliver's Final Score would have been twice Gordon's.

How many frames did each win, and what was the score in the final frame?

Answers initially by PM please.

[abextra]

Round 268 - 10k-ball pool

I just played a frame of a new game that I had invented, called 10k-ball pool. There are 10,000 balls on the table, numbered from 1 to 10,000, and the white.
......

I just made a break of 147147147147 - and the first 6 balls I potted in my break were each numbered lower than 50.

What were those first six balls? And the 7th ball?

d_g, did you make this break with 7 balls only?

[davis_greatest]

Yes, very nice, abextra. Congratulations!

I am not sure what the maximum possible is or whether those can be beaten - I won't formally close the round in case anyone wants to try to find higher, but I haven't got any more triangles than that!

[abextra]

14 + 18 = 32 from me

(and 2 triangles with 4 brown lines, hope I counted correctly this time ).

[Semih_Sayginer]

Yes, and yes, that is why it's in the lead!

thanks, thats why i asked....

[snookersfun]

13 and 16
cues#1a.jpg

[davis_greatest]

is it not the only reply, so obviously in the lead? (just asking)

Yes, and yes, that is why it's in the lead!

[Semih_Sayginer]

OK, 11 + 14 = 25 is in the lead!

is it not the only reply, so obviously in the lead? (just asking)

[davis_greatest]

OK, 11 + 14 = 25 is in the lead!

Can anyone else better (or match) it?

[Monique]

302-final.bmp

9 lines 14 triangles.

scan10001vi7.jpg

8 lines 11 triangles (1,5 and 14 disappeared)

[davis_greatest]

Round 273 - More lines

... as for round 271 http://www.thesnookerforum.com/showp...postcount=2510

but now two diagrams needed - one with 8 lines and one with 9 lines.

Bids and diagrams to go directly on the thread please...

[davis_greatest]

Congratulations, Monique - one-half (50%) is the correct answer!

The easiest way to see this is to observe that, because Gordon has one more ball than Charlie, he must have (with 100% likelihood) either more pinks or more browns (but can't have more of both, as he only has one ball extra).

Since each possibility is equally likely (by symmetry), the probability that Gordon has more pinks is 50%, and the probability that Gordon has more browns is also 50%.

[Monique]

Round 272: 1/2

reasoning:
P(Gordon has more pinks) = P(Gordon's last ball was pink)*P(Gordon had as many pinks as Charlie or more before taking the last ball) + P(Gordon's last ball was Brown)*P(Gordon had more pinks than Charlie taking the last ball)

Now P(Gordon had more pinks than Charlie taking the last ball)=P(Gordon had more browns than Charlie taking the last ball) because both occurences are equally plausible

So:P(Gordon has more pinks) = 1/2*P(Gordon had as many pinks as Charlie or more before taking the last ball) + 1/2*P(Gordon had more browns than Charlie taking the last ball) = 1/2*P(Gordon had as many pinks as Charlie or more before taking the last ball or Gordon had more browns than Charlie taking the last ball) = 1/2*1

[davis_greatest]

Very nice pictures!! Thank you abextra and snookersfun - and congratulations for the winning bids of 24 points!

No answers / explanations (or even guesses) to round 272? I'll have to answer it myself soon!