Puzzles with numbers and things

[abextra]

...and while I am here, I shall put Monique's beautiful artwork to R.242 up:

Well done, Monique, it's really beautiful!

Here's my pic for Round 247 , 11 rows and 11 columns, the value of coloured balls adds up to 9 in each of them... ... you only have to count the balls in horizontals and verticals, not in diagonals.

4 . 0 . 0 . 2 . 0 . 3
. 3 . 1 . 0 . 0 . 5
1 . 4 . 1 . 1 . 0 . 2
. 1 . 6 . 1 . 1 . 0
0 . 1 . 5 . 1 . 2 . 0
. 0 . 1 . 7 . 1 . 0
0 . 2 . 1 . 4 . 1 . 1
. 0 . 1 . 1 . 6 . 1
1 . 2 . 1 . 1 . 4 . 0
. 5 . 0 . 0 . 1 . 3
3 . 0 . 1 . 0 . 2 . 3


I still hope Barry likes this arrangement... and don't forget how much Gordon likes bananas!

[snookersfun]

I still hope Barry likes this arrangement... and don't forget how much Gordon likes bananas!

wow, very creative...and rather squareish Another nice pic!

[Monique]

Finally got that 280 for Round 253, and 278 an 277 also ... well anything but 279

[snookersfun]

Finally got that 280 for Round 253, and 278 an 277 also ... well anything but 279

see? Join the club
Well, guess you could do a 279 (in a bit of silly version of the 280)...

[davis_greatest]

Thanks for all the answers so far to rounds 248 to 253... I will get to them all, but unfortunately can't tonight! (Sorry! )

I think there have been plenty of correct answers (mainly from abextra, Monique and snookersfun!) to rounds 248, 249, 250, 251 and 252. So, well done! (I shall list them all.)

Also some high bids to round 253! It looks like the highest bid submitted for round 253 is 280 (unless I've missed one), found by snookersfun, abextra and Monique! 280 is a good bid, but (slightly) higher is possible!

[abextra]

... 280 is a good bid, but (slightly) higher is possible!

Hehehe... how did I know it's coming! Ok, I bid 281... (sent out the explanation, hope there are no mistakes ).

Welcome back, d_g!

[snookersfun]

Hehehe... how did I know it's coming! Ok, I bid 281... (sent out the explanation, hope there are no mistakes).

Welcome back, d_g!

lol, yes that 280 was too easy..., so 281 as well!

and welcome back

[Monique]

Oh yes ... 281

[davis_greatest]

I still hope Barry likes this arrangement... and don't forget how much Gordon likes bananas!

Yes, nice picture! Very pretty!

We have had the maximum possible bids - well done! ....so I'll invite all the answers for rounds 248 to 253 that have been sent to me to be posted on the thread...

[davis_greatest]

While those are coming up, a quick one for those who dislike a bit of probability.

Round 254

In the Premier Ape League, matches consist of 6 frames.

It doesn’t matter who wins – all that matters is the score. This means that there are four possible final scores: 6-0, 5-1, 4-2 or 3-3.

In each match, each player in a pair has a fixed chance of winning any given frame, and each frame is independent of all those that come before.

(a) When Rocketsalad plays Dragonfire, they are evenly matched (50% chance each of winning each frame). What is the most likely final score and how likely is it?

(b) (harder) When Nuggins plays Windywhirl, Nuggins’s superior skill makes a 4-2 final score (which could be to either ape) exactly 3 times as likely as a draw. What is the chance that they will share the first two frames?

[davis_greatest]

ok, mine eventually was this here:
701000120
160011002
026110010
202510010
011351000
011035001
100000433
000103241
010101404

We have to use coloured balls adding up to 99 points, meaning that those can be arranged in a minimum of 9 lines X 11 points each. Thus the smallest possible square is one of 9x9=81 balls.
As we have 43 value balls, we need 38 white 'fillers', therefore we are in for 201-38=163 bananas...

... and I don't have my 163-banana offering any more, but I think the arrangement was pretty similar to that one!

If you keep the balls as a "squashed" rectangle, with all the rows and columns aligned, then the 163 bananas is the best possible - but as abextra showed very nicely, more bananas are possible with more creative spaced out arrangements!

[Monique]

R250 solution ...

[Monique]

R248

[Monique]

R249

[Monique]

Round 251 for a break of 323:

All colours are supposed to be potted in "their" pocket except when specified.

R-6,R-11,R-9,R-7,R-8,R-10,R-6,R-11,R-9,R-7,R-8,R-10,R-6,R-11,R-9,2,3,4,5,6,7,8,9 (in 4),10(in 6),11