Puzzles with numbers and things

[Monique]

R164 closing ...

Mr Grott is extremely unhappy because he (and only he) was not kissed by the delicious Tallia Mabb. The fact that he got no WhiteChocolateGlove is relatively less important
Rollie stands 21 th in the line, and got 3 DarkChocolateBalls; all the others got only 2.

As D_G said, this is the first time Grott leaves this thread without slaps ... he leaves it without a kiss. Which is worse is disputable. Maybe we should launch a poll?
Have a nice day everyone

[davis_greatest]

Round 167 - Who's got the balls?

This evening, I went to play snooker. However, it was a rather boring affair and I struggled to make any sizeable breaks, as all the balls were missing. Eventually, I found them - my three apes were playing with them and had shared them out.

They had, among them, the complete set of 22 balls, and each ape was adding up the value of his balls (1 for a red, 2 for a yellow, 3 for a green etc, with no value for the cue ball).

Although my pet gorilla Gordon had the fewest balls (and Oliver, my little pet orang-utan had the most), the value of Gordon's balls was at least 3 times the value of my pet chimpanzee Charlie's. Nevertheless, the value of Charlie's balls was at least as great as Oliver’s.

What balls did each ape have?

[davis_greatest]

apologies for being so ignorant, its just cant grasp the concept of this being represented by a picture, as they arent square angled triangles but equilateral ones.

Welcome to the thread, icantplay.

The principle is illustrated in the pictures in snookersfun's message 4 posts up.

The picture on the left shows equilateral triangles, as the packs actually appear on Chimpanzicus, Gordonicus and Olivero.

The picture on the right shows the triangles with the same number of reds, but just "shifted" into a right-angled triangle. The shifting does not change the number of balls in any of the triangles - it simply makes the parallelogram for the pack on Davisgreatus turn into a rectangle, in order to make it easier to see the correspondence.

That is, the two pictures are the same, except that the one on the left has the rows centred, whereas the picture on the right has the rows left-aligned.

[icantplay]

apologies for being so ignorant, its just cant grasp the concept of this being represented by a picture, as they arent square angled triangles but equilateral ones.

[Lee Vilenski]

Thank god, maybe I'm just so stupid that it's working in reverce?

[davis_greatest]

....don't worry, if you still haven't figured it out -
see quote:

A claim that often accompanies these instructions is that the smarter an individual, the greater amount of difficulty the individual will have in solving it. If such a statement is true, it may be attributed to the fact that "smarter" people tend to be more knowledgeable in a wide range of information which they may unnecessarily attempt to draw upon to solve the puzzle.

Good! I must be very smart then because I have no idea at all! How embarrassing for Monique, having solved it already.
Next guess: 2

[snookersfun]

the petals around the rose are neither 0 nor 15 So, this one still needs closer bids...

the proof to round 166:

Algebra:
number of balls in 'smaller' triangle + triangle with 2n rows + rectangle = #balls on chimpanzicus
n(n+1)/2 + 2n(2n+1)/2 +n*2n= a(a+1)/2 (with a=147147147147147))

so: 9n^2+3n= a(a+1)
or 3n(3n+1)=a(a+1)

thus 3n=a or n=a/3

(and more triangles with smileys (by special invitation) to show that)

[April madness]

yes, Monique... and ODD

[Monique]

fifteen!

yeah, I'm odd... that's why

LOL April you're persistent!

R166 picture solution



If too small look up the Gallery ...

[April madness]

.....zero?

fifteen!

yeah, I'm odd... that's why

[davis_greatest]

Round 166 - Intergalactic packs

Grandfather Charlianus, on the planet Chimpanzicus, is giving his grandson Trumpo a lesson in intergalactic sport.

“Snookum, my dear Trumpo,” says Charlianus, “being the greatest sport in the universe this side of Andromeda (and the other side too), is played all over the universe, although there are slight variations from how we play it here.”

“Like what variations?” asks baby-faced Trumpo.

“Well,” said Charlianus, “of course, everywhere it is played with a white and six colours and a pack of reds, but on some planets, due to problems with gravity, they use fewer reds in the pack at the start of the frame.”

“Fewer reds?” asked Trumpo. “Like how many?”

“Well,” replied Grandfather Charlianus. “On Planet Earth, for example, they call snookum “snooker” (or snukker for those who won the Earth Championships in the year 400000001979) and the triangle of reds has only five rows!”

“Only five rows?!” exclaimed Trumpo. “But our triangles of reds here on Chinmpanzicus have 147,147,147,147,147 rows. I thought that was standard. Even that seems very small. Five rows sounds ridiculous! That must mean the frames on Earth are over in a flash.”

“No,” replied Charlianus. “because they play very, very slowly. I once watched a frame on Telescopivision and, even with only five rows of reds in the triangle, the guy took 5 minutes and 20 seconds just to clear the table once! And that’s Earth minutes and seconds!”

“Wow!” said Trumpo. “That IS slow. What was he doing? Sleeping? What about on other planets?”

“OK,” said Charlianus. “When they play snookum on the Planet Gordonicus, the triangle of reds is bigger than that on Planet Earth, but it’s still pretty small.”

“How small?” asked Trumpo.

“Well, put it this way,” said Charlianus. “The triangle of reds on Gordonicus has only half as many rows as the triangle of reds when they play on the Planet Olivero.”

“So how many rows of reds in the pack on Olivero?”

“The same number of rows,” explained Charlianus to the youngster, “as the pack of reds on the planet Davisgreatus.”

“So there are the same number of reds in a pack on Olivero as on Davisgreatus?…” began Trumpo.

“No,” said his grandfather.

“But you just said….”

“I said there are the same number of rows in each pack. But I didn’t say that the pack is a triangle on every planet! On Davisgreatus, the reds are not arranged in a triangle! There, and only there, the reds are arranged in a rectangle!”

“Oh my!” said Trumpo, getting more and more confused. “And how many columns of reds does this blooming Davisgreatus rectangle of reds have then?”

“Well, here’s the funny thing,” said the old chimp. “The number of columns in the rectangle in the pack on Davisgreatus is the same as the number of rows in the triangular pack on Gordonicus!”

“This is getting confusing,” said Trumpo. “So how many is that?”

“Well, Trumpo,” said his grandfather. “The number of reds at the start of a frame of snookum here on Chimpanzicus is the same as the total number of reds at the start of frames on Gordonicus, Olivero and Davisgreatus combined! So you tell me!”


And so…. (with no calculators or computers)… help Trumpo and tell him how many columns in the rectangle in the pack of reds in snookum on Davisgreatus!

Congratulations to snookersfun, Monique and austrian_girl for finding that the number of columns in the pack of reds on Davisgreatus is one-third of the number of rows in the triangle on Chimpanzicus.

Since one-third of 147 is 49, one-third of 147,147,147,147,147 is 49,049,049,049,049.

Incidentally, this little puzzle relies on the fact that, if T(x) is the x-th triangular number,
i.e. T(x) = 1+2+3+4+5+...+x, then

T(x+y) = T(x) + T(y) + xy

Here the number of rows in the pack on Gordonicus was x, on Olivero was y, and on Chimpanzicus was x+y. You were also told that y=2x. Therefore x is one-third of x+y.

This can be shown either with algebra or seen intuitively by drawing a picture. Explanations from those who solved it (or from anyone else) are invited here on the thread.

[davis_greatest]

.....zero?

[snookersfun]

Yep, its 4.

the consensus (d_g, Qubit and dantuck) on this one seems to be that it is 4, and it is indeed

so one more, roll#5 (last one?) and don't worry, if you still haven't figured it out -
see quote:

A claim that often accompanies these instructions is that the smarter an individual, the greater amount of difficulty the individual will have in solving it. If such a statement is true, it may be attributed to the fact that "smarter" people tend to be more knowledgeable in a wide range of information which they may unnecessarily attempt to draw upon to solve the puzzle.

[Qubit]

Yep, its 4.

[davis_greatest]

OK, no ideas yet, so a guess: 4