Puzzles with numbers and things

[Monique]

R336 - Number Cruncher, a very easy one

NumberCruncher1.JPG

good luck!

[Monique]

R335 ... update

Snookersfun solved it already ... Well done!
And Ja. also! Congrats
See ... a bit tricky but not that difficult

[Monique]

Round 335 - Pot Square

Barry the Baboon is back from hols in Belgium and is very excited about a new billiard game he just discovered: "Pot Square". It must be said that it rained a lot so he spent plenty of time in various pubs and halls
He's explaining to Charlie how to play it…
"See, you play on a snooker table and you have 32 object balls, 16 yellows, numbered from 1 to 16, and 16 greens also numbered from 1 to 16. Both yellows and greens are arranged in a square pattern and both "squares" are placed symmetrically with their centre aligned with the pink spot and the yellow and green spot respectively. Each player has his/her own cue ball, one white placed on the yellow spot and one black placed on the green spot. At the beginning of the game the ref draws who plays with what colour. Then both players have to wait in their seats until the ref lets of a cracker and then … then they rush to the table and the first one who pots all his/her balls in order wins! The balls have to be arranged in the squares in a well defined order though. The yellows are just in order …
01 02 03 04
05 06 07 08
09 10 11 12
13 14 15 16
The greens are like this …. eerh I can't remember …
09 04 ?? ??
?? ?? ?? ??
?? ?? ?? ??
?? ?? ?? ??
What I do remember however is that for any pair of numbers 1 to 16, the chosen pair will be in a row, column, or main diagonal in exactly one of the two squares, the yellow or the green and … oh yes the sum of values of the balls is the same in each row, each column and the diagonals on the green square.
And Charlie arranges the green balls…. How?:snooker:

[snookersfun]

R. 334: adding up to squares

Gwenny is given her first snooker lessons, after a bit of practice she manages to pot the odd ball and even manage a max break of 15. One session she notices that she strangely enough made breaks of 1-15 once each, moreover she made them in such a way that each two consecutive breaks add up to a square number.

Please give the sequence of breaks (PM)

Thought I update quicker this time around: Mon solved this in no time, so see is an easy one Well done MON!!
Hoping for more customers now!

[snookersfun]

R. 333: reds around blacks

Oh dear, left that open forever again. Well on the other hand there is only still one answer to it (but a long time ago) from Monique. Well done Mon!

Anyone else feels like trying it? A little hint: looking at the last row, one can immediately position 2 red balls (as they need to neighbour black balls but can't touch each other) to start out...


or maybe an easier one:

R. 334: adding up to squares

Gwenny is given her first snooker lessons, after a bit of practice she manages to pot the odd ball and even manage a max break of 15. One session she notices that she strangely enough made breaks of 1-15 once each, moreover she made them in such a way that each two consecutive breaks add up to a square number.

Please give the sequence of breaks (PM)

[abextra]

Thank you again, Monique!

I got confused when I saw there are more than one possible solutions - I thought I've misunderstood the question and stopped trying.

[Monique]

Monique, thank you so much for the explanation!
Congratulations to davis_greatest, Snookersfun and Ja!



May I ask - would score 109-37 work for frame 2?
(Charlie takes 5 reds with colours, then fouls, giving 4 (or more) points to Rollie, Rollie then pots ten reds with colours and the final colours?

Of course! you are right ... that would be another possibility for Frame 2 with a score of 146. That wouldn't make it 4-0 though as only one foul was made by Charlie. Well done.

[abextra]

Monique, thank you so much for the explanation!
Congratulations to davis_greatest, Snookersfun and Ja!

All credit to D_G who came up with a solution for a frame score of 146

3-0 to Rollie with total points of 146 each frame:
Frame 1: 79-67 (A way for the 79-67 score would be if Charlie potted 8 reds and blacks (64);then Rollie 7 reds (6 with blacks, one with pink), followed by yellow (57); then Charlie the green (3); then Rollie cleared from brown to black (22).
Frame 2: 127-19 (Charlie pots 3 reds with colours for the 19 and then fouls, giving Rollie 4. Rollie then takes 12 reds with blacks and the 6 colours)
Frame 3: 139-7

May I ask - would score 109-37 work for frame 2?
(Charlie takes 5 reds with colours, then fouls, giving 4 (or more) points to Rollie, Rollie then pots ten reds with colours and the final colours?

[Monique]

Time to close Round 329...

Rollie O'Sunnyman just won the 2008 Chimps&Bonobo World Chimpionship, withewashing an out-of-form Charlie.
It was quite a remarkable match. Rollie's points score increased frame after frame and he made a century taking all the colours in every frame but the first one. Moreover the total of points scored was exactly the same in each frame, and the points scored by both players were all prime numbers.
There was just one foul, made by Charlie in the second frame, during the whole match and Rollie's highest break was 139…

What is the final score of that match and what are the points scored for each frame, knowing that the total number of points scored in each frame is the highest possible under the conditions?

Post-match press conference summary:

Charlie was gutted. He said Rollie was sooooooo terribly slow he got bored and couldn't handle the situation. He was also hungry and the sight of the trophy, nicely on display, was making things worse and got the better of him. It's a shame really said Charlie because this is also a team event and until the Final the Chimps and the Bonobos were tied up each team having won the same number of matches.

Rollie who was playing for the Bonobo team was delighted to win this title. "That's one my good old rival Henry Steven never got!" he said smiling broadly. He also confessed he would share the trophy with his team mates … but couldn't resist taking a bite at it on the spot!

[ATTACH]1435[/ATTACH]

Rollie celebrates after winning the 2008 Chimps&Bonobo World Chimpionship.

Time to close R237 and R238 ... answers on the thread anyone?

All credit to D_G who came up with a solution for a frame score of 146

3-0 to Rollie with total points of 146 each frame:
Frame 1: 79-67 (A way for the 79-67 score would be if Charlie potted 8 reds and blacks (64);then Rollie 7 reds (6 with blacks, one with pink), followed by yellow (57); then Charlie the green (3); then Rollie cleared from brown to black (22).
Frame 2: 127-19 (Charlie pots 3 reds with colours for the 19 and then fouls, giving Rollie 4. Rollie then takes 12 reds with blacks and the 6 colours)
Frame 3: 139-7

As a "best of 5 format" is unlikely for a final and, slow as Rollie is, Charlie wouldn't probably be ravenous after just 3 frames ... 144 yields an interesting solution with a score of 6-0 or 7-0 ...

Relevant couples of primes having a sum of 144 are
5 139
7 137
13 131
17 127
31 113
37 107
41 103
43 101
47 97
71 73

If the first column represents Charlie score and the second Rollie's, then the couples in bold require a foul from Charlie because Rollie makes a century and takes all the colours in every frame but one. (obviously the first one.)
41-103 and 43-101 are not valid because Rollie makes a century in every frame but one, and with Charlie fouling he can only make 99 and 97 breaks there. As only one foul is made by Charlie, in frame two, the 17 - 127 couple must be disregarded also.

This leaves us with the following scores

F6 5 139
F5 7 137
F4 13 131
F3 31 113
F2 37 107
F1 47 97 or 71 73

In F2 Charlie fouls and Rollie makes a century of 103. However, the same score can be achieved without a foul ... so if the sentence "Rollie's points score increased frame after frame" is interpreted in a "non-strict" sense, we could have a 7-0 score with frames 2 and 3 having identical score points (but a higher century for Rollie in frame 3)

Well done Snookersfun and Ja!.

[snookersfun]

R321 - (a) 9 and (b) 22.
Might be possible to find more than 22 for (b) using lines that give fewer than 9 for (a), but I doubt it.

well, well, missed one composite... yes, 22!
well done d_g! Late entry nipping the lead there!
Are we going to get a drawing and the solution?


and while I am here:

R. 333: reds around blacks

The following drawing shows part of a snooker table partioned by a grid. Several black balls are placed on it.
2 reds next to-1.bmp
Your task is to place additional red balls, exactly two reds surrounding each black (touching grid of black ball at edges or corners). Reds though are not allowed to touch (even diagonally).
The numbers on the side of rows and top of columns give total amount of reds in each respective row/column.

Answer by PM please (position of reds can be given by letter/number combinations as well)

[davis_greatest]

R321 - (a) 9 and (b) 22.
Might be possible to find more than 22 for (b) using lines that give fewer than 9 for (a), but I doubt it.

[snookersfun]

Round 332 obviously: up to 3 correct entries so far.

Congratulations d_g, Monique and Robert!

Next answer on the thread then...

[Kathrin]

do you mean R322 balls in bags? I thought this is already solved

[snookersfun]

Anyone not confused right now

onebody wasn't!
I do have one correct answer to R. 332 now
...and one attempt
although, forgot to mention, answers by PM please!

[Kathrin]

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.

Anyone not confused right now