Puzzles with numbers and things

[snookersfun]

...and meanwhile, back to balls:

R. 332: counting balls

Oliver and Gordon, rather bored by now, sit together one day and start to play around with their snooker balls. Initially both start out with a certain amount of balls each and then each add one ball at a time (and kind of simultaneously) to their previous amount to try to built nice geometrical figures (as usual, mainly triangles or pyramids).

Charlie is observing them from the side and at one point comments to Gwendoline: Do you know what? Gordon right now has as many balls as Oliver will have, when Gordon will have twice as many balls as Oliver had when Gordon had half as many balls as the sum of their balls now. Also Oliver has as many balls now as Gordon had when Oliver had half as many balls as he will have when he takes 10 more balls.

How many balls do Gordon and Oliver have at the time that Charlie is making his observation?
(I hope I didn't confuse myself translating this into snooker/ape talk) Good luck!
chimp.jpg

[snookersfun]

I think I have a 9 and 21 ...

sounds excellent (at least I couldn't find more). 9 is probably the max one can find for (a)

I think we can start putting up drawings on the thread now (even for the lower bids)

Also non-bidders are invited!

[Monique]

I think I have a 9 and 21 ...

[snookersfun]

OK, next bids a) 8; b) 19.

yes better, but...

not quite there yet
(both (a) and (b))

[davis_greatest]

OK, next bids a) 8; b) 19.

[snookersfun]

I'm sure much higher must be possible, but to get things going, opening bid of 7 for (a).

and those lines would give (b) 18 triangles

very nice opening bid, but...
both a) and b) can be bettered

[davis_greatest]

I'm sure much higher must be possible, but to get things going, opening bid of 7 for (a).

and those lines would give (b) 18 triangles

[davis_greatest]

Round 331 opening bid

I'm sure much higher must be possible, but to get things going, opening bid of 7 for (a).

[snookersfun]

Just had a look at this. There won't be any advances on 35 because there are exactly 35 possible triangles. So, congratulations Robert

right, so closing R.330 now. Well done Rob.

...and R. 331: even more (or less) triangles

this time start out with a capital letter M (possibly bigger than this), add three more straight lines and count how many triangles you can find in the resulting figure.

Please but your best bids up on the thread, for highest number of triangles found:
a) counting simple triangles only (no other lines inside the triangle)
b) including composite or overlapping triangles

[davis_greatest]

Also, if there are no advances on the 35 triangles, we can close this round

Just had a look at this. There won't be any advances on 35 because there are exactly 35 possible triangles. So, congratulations Robert

[snookersfun]

Yeah it's very easy to do. I use GIMP image editor (photoshop type thing but free), make the image up with lots of layers, then when I choose to save as a gif it gives me the option to either flatten the layers or save them as an animation.

Anyway, here it is again.

...improved by counting now as well.
Yes, indeed thanks for the explanation. I will definitely have a go at it sometimes, much more sophisticated than the doofus way I came up with yesterday (loading up lots of frames (created in paint) into a web-based gif animator thingy (which, mind you, I was quite proud of at the time)

Also, if there are no advances on the 35 triangles, we can close this round

[abextra]

Great animation, Robert, very well done! Thank you for the explanation!

I am impressed!
Can I give that the best attachment prize in this thread?

I think you can, even more, I think you must!

[Robert602]

Yeah it's very easy to do. I use GIMP image editor (photoshop type thing but free), make the image up with lots of layers, then when I choose to save as a gif it gives me the option to either flatten the layers or save them as an animation.

Anyway, here it is again.

[snookersfun]

Can't see any more, think I might've miscounted last night (or counted some 4/5 sided triangles). My bid stands at 35 then, I'll repost that attachment after a bit of snooker (brother's calling) if no one wants to advance on that.

yes, make sure you put that neat attachment back up later on
(edit: btw. how did you do it? was that a gif thing?)

[Robert602]

Can't see any more, think I might've miscounted last night (or counted some 4/5 sided triangles). My bid stands at 35 then, I'll repost that attachment after a bit of snooker (brother's calling) if no one wants to advance on that.