Puzzles with numbers and things

[snookersfun]

OK, the answer, I have this nice picture here, which might explain it a bit easier than words...
Although words first:

1) the total weight of the balls along the shorter side of the rectangle is 147899g = 131g x 1129 balls (prime factors)

2) starting with two triangles (-1 ball each), one has:
2(n(n+1)/2-1) = n²+n-2 = (n-1)(n+2) {n being the base of the triangle}

meaning that one can always form a rectangle with one side a ball shorter than a (complete) triangle and the longer side 2 balls longer than a triangle.
As n-1=1129, n+2=1132, which leaves 1131 rows remaining after taking one row of.

[Lee Vilenski]

Wow, I nearly got there..

[Monique]

R164 SnookerSnoops Candy Fest

This is not difficult, just a bit obfuscated ...

Once upon a time in a Belgian dream ...
The day before the opening of the first Belgian Open, the famous candy manufacturer and sponsor of the tournament, SnookerSnoops organizes a promotional event. In front of a pack of photographers, the players are invited to line up. Unfortunately Mauny Church declined because he is on a diet, so that only 31 players are present. And, of course Mr Grott is last in the line as he arrived just in time and a bit untidy after missing his connexion in Heathrow...
Famous referees Mr Jess Vanraas and Mrs Tallia Mabb will distribute Snookersnoops candies to the players while photographers take a lot of pictures.

The following candies have been supplied:

WhiteCocoBall: 13 boxes of 147 items
BitterChocolateBall: 9 bags of 7 items
CreamyStrawberryBall: 7 bags of 6 items
BlueMintBall: 11 bags of 5 items
CoffeeToffeeBall: 17 bags of 4 items
WhiteChocolateGlove: 15 bags of 2 items
SourAppleBall: 19 bags of 3 items
JuicyLemonBall: 35 bags of 2 items
RedCherryBall: 28 bags of 15 items
LiquoriceCue: 15 boxes of 50 items
CrispyWafferRest: 3 boxes of 147 items

Jess starts the distribution of candies giving out the items one by one, to each player in turn, moving from the first player to the last one, as many times as necessary. This of course takes a while. So that, after the CoffeeToffeeBalls, Jess needs a break, and much to the delight of the players, Tallia takes over. Each WhiteChocolateGlove is being offered with a kiss. The pleasant interlude is only too short and Jess resumes with the SourAppleBalls, the JuicyLemonBalls, etc... untill the quasi exhaustion of the candies supply. In fact Jess eats the last CrispyWafferRest himself!

At the end of the distribution, it appears that Mr Grott is extremely unhappy. He claims that once again he, and only he, has got an unfair treatment. SnookerSnoops however insists that each player has received exactly the same number of candies.
As for Rollie O'Sunnyman, he is in high spirits. In his post distribution interview he explains that he was lucky enough to receive one more of his favourite SnookerSnoop sweet than any other player!

Why is Mr Grott so unhappy?
What's the position of Rollie in the line?

"Experts" answer by PM, please ...
Mr Grott appears courtesy of Davis_Greatest. Thanks D_G.

[Lee Vilenski]

Gave a pm. Wouldn't be surprised if I was way off!

[davis_greatest]

Hehe, great question Monique

I don't know why Grott is moaning again - this has to be the first time he has left this thread with sweets rather than slaps. For future questions, remember that he prefers slaps.

I'll PM you too...

[dantuck_7]

On R163 why does the weight have to be 131g? 37g seems more sensible to me and the rectangle of balls would be 3997 by 4000 which is arguably 'squarer' than the above solution.

As for R164 I'm going to have to read it ten times!!

[davis_greatest]

On R161 why does the weight have to be 131g? 37g seems more sensible to me and the rectangle of balls would be 3997 by 4000 which is arguably 'squarer' than the above solution....

You mean Round 163?

Well, the row of balls weighs 147.899kg = 147899 grams, and 147899 is not divisible by 37.


Edit: Oh, I see what you've done! You misread the question, and thought that it was 147.889kg instead of 147.899kg?

[dantuck_7]

Oops - I've factorised 147889

= 37 * 3997.

[snookersfun]

oops indeed Dan

I found us something nice and easy, but this will come in installments, like a new picture a day...

Petals Around the Rose

The name of the game is Petals Around the Rose, and that name is significant. Every answer in this game is zero or an even number.

for example in Roll #1 the answer is two.

Now you are supposed to tell me the answer for the next rolls, before I tell you. Whoever has an idea can put up the answer on the thread, but without explaining the theory behind it! If you figure it out, you don't want to give the idea away to the others. Make them work for the answers, too.

OK, anybody with advances on a possible answer for roll#2?

[davis_greatest]

No idea, snookersfun, but my opening guess is 4.

[snookersfun]

nice opening bid, let's collect bids for now....
(not that I expect anybody to get it at first try really- i.e. given only the answer of that first roll)

[April madness]

I guess 5

[Qubit]

My guess is 8

[Monique]

R164 status and a guess ...

R164 has been solved by Snookerfun and Davis_Greatest (of course!) Congratulations!
It remains open ...

R165 wild guess: 0

[Lee Vilenski]

It'll be 6.