Puzzles with numbers and things

[dantuck_7]

Have we lost some posts here?? Think I remember seeing some answers to 418 once upon a time?!

[Monique]

Take it the balls are numbered 1 to 9?

Yes, of course, they are. Sorry for not being explicit.

[dantuck_7]

Take it the balls are numbered 1 to 9?

[Monique]

Round 418 ... Nine balls

Charlie and Gordon got home very late all excited and giggling, alledgedly from the pool hall. Talia Mabb suspects that they have had more Banana cocktails than they have played racks
"What have you been up to?" she asks. "Oh playing 9 balls" says Charlie (angelic look there). "Yes, with an exciting variation" add Gordon. "Really?" says Talia. "Yes" says Gordon, "Instead of putting the balls in a diamond shape for break-off, we put them in a triangle, like this"

OOOO
OOOOO
OOOOOO
OOOOOOO

"And you know what?" adds Charlie "In each rack we played, we managed to put the balls in such a way that the sum of the "ball numbers" was the same for all three sides of the triangle AND the sum of the squares of the "ball numbers" was the same for all three sides of the triangle also" ...

"And those sums were different for each rack I guess?" asks Talia. "Of course" says Gordon (very proud).

"That's what I thought" says Talia wagging a finger at the pair.

How many racks did they play?

Answers by PM...
and, this can be solved by "brute force" using programming of course, but it can be solved in a more subttle way also

[Monique]

Some people really have too much time on their hands ... facinating thread though and somewhat mind boggling in places even though I have A level grade A's in 4 math based subjects.....

Going to have to think back a long way to come up with some puzzlers that will perplex you lot!

We'd love that!

[bkpaul]

Some people really have too much time on their hands ... facinating thread though and somewhat mind boggling in places even though I have A level grade A's in 4 math based subjects.....

Going to have to think back a long way to come up with some puzzlers that will perplex you lot!

[Monique]

Yes, indeed. Box A has a volume of 48 sq inches while box B only has 35...

Well done

[dantuck_7]

Box A has dimensions 2x4x6 inches.... and B is 1x5x7 inches. So A would be the choice as it will hold more chalk!?!

[Monique]

No one?

[Monique]

Round 417 ... box story ...

Barry the baboon is doing promotional work: all customers answering correctly all the 147 questions of his snooker quizz are entitled to a box full of chalks, free!
Davy Steves has just done that and now Barry his telling him "Great! Congratulations! Now you have to chose which model of box you want, model A or model B?"
"How would I know?", says Davy, "Can I see them?". "No" answers Barry "however I'll tell you this; both boxes are regular boxes with rectangular faces and all and I will give you the three "perimeters" for each ... box model A has perimeters 12, 16, and 20, and box model B has perimeters 12, 16, and 24, all in inches of course "

Davy now smiles broadly. Which model will he chose and why?

here is how Barry measured the perimeters...

cuboid.gif

[Monique]

Two correct answers in already. One from snookersfun and one from Krypton

Well done both and a very heartfelt welcome to our new puzzler!

update ... moglet got the correct answer also ... But I gave him some additional homework

[Monique]

R416 - puzzling!

The apes are bored ... so Charlie comes up with a little brain teaser:

"Let's suppose", he says, "that we have x^2 + x + 1 = 0. So what's the value of x^3?"

I takes only 3 seconds to Gwenny, Oliver and Gordon to come up with the answer

Rollie and Barry look genuinly puzzled though. "Oi, that ain't possible", says Rollie

"Oh yes it is!" exclaim the four others

What's the answer? What's Rollie's problem? What's the explanation?

[moglet]

R415,

Blind as a bat as usual

In my "table" there is another "spare" frame right at the bottom where 78 is scored twice, so scoring visits of 1 and 2 could be included here and still have a minimum of 78 frames to cover every "break"!!

[Monique]

Aaaarrrghhhh ... can't see much from Internet cafe ... can't read the attachment.
I'm affaid I'll have to leave R415 mainly in your hands guys.

[moglet]

R415

I can see no advantage in using the free ball more than twice in any frame. I've assumed a minimum break of three as the official Rules of Snooker definition suggests in Section2,8 "...a number of pots in successive strokes..." However, there are two "spare" frames one of which could be used to score 1 off a freeball, unfortunately to score 2 we have to use at least 1 red, this would require a whole frame just to make the 2 pt score.

If my thinking is correct the table should be self explanatory: