Puzzles with numbers and things

[snookersfun]

Round 177: combined high breaks
a nice and easy one to start the week:

OK, to make that snooker related: Let's say seven of my cats are comparing their high breaks in snooker. Lacking opposable thumbs, they aren't nearly as good as d_g's apes though (but better than me), so they decide to count some combined efforts in order to show off with century break like numbers.

So we have those seven high breaks of A, B, C, D, E, F, and G.

When all these numbers except A are added together, 116 is obtained.
When all these numbers except B are added together, 122 is obtained
When all these numbers except C are added together, 123 is obtained
When all these numbers except D are added together, 108 is obtained
When all these numbers except E are added together, 110 is obtained
When all these numbers except F are added together, 119 is obtained
When all these numbers except G are added together, 100 is obtained

Find each of the seven numbers.

Expert's answers by PM, otherwise on here...

[Monique]

R175 closing ...

The answer is 1992.

Highest and lowest centuries of the Belgian Open were "monochromatic" total clearances. Possible values are 102, 117, 132, 147 and so the number of centuries must be 16, 31 or 46. As this number must be a square only 16 is valid. So 16 centuries were made by 4 players, making 4 centuries each.
Now, one of the centuries' score is 2 times the number of centuries times the number of 'century' players, so 128. Therefore the 16 centuries scored between 117 and 132 points and the sum is 1992

[davis_greatest]

First in to name the colour correctly was snookersfun! Congratulations! The round is still open though!...

Monique has joined snookersfun as a solver of round 176! Congratulations!

It is much easier than might appear at first sight, and will remain open until 9.30a.m. BST tomorrow...

[dantuck_7]

I'm off to see the cricket at Lords today - maybe tonight...

[snookersfun]

1A 111
3A 21
4A 13
6A 33
8A 13
9A 232
1D 11
2D 11
3D 213
5D 323
7D 32
8D 12

Should be easier to read this time.

Yes! perfect! So, we can close round 174
I'll give you one more day for round 173 then, as you got this one, the other one shouldn't be a problem

[davis_greatest]

Should be easier to read this time.

TRUE, TRUE!

[dantuck_7]

1A 111
3A 21
4A 13
6A 33
8A 13
9A 232
1D 11
2D 11
3D 213
5D 323
7D 32
8D 12

Should be easier to read this time.

[dantuck_7]

My answer to R174:

1A 111 3 111 1 TRUE
3A 21 2 21 2 TRUE
4A 13 2 13 3 TRUE
6A 33 2 33 4 TRUE
8A 13 2 13 5 TRUE
9A 232 3 232 6 TRUE
1D 11 2 11 7 TRUE
2D 11 2 11 8 TRUE
3D 213 3 213 9 TRUE
5D 323 3 323 10 TRUE
7D 32 2 32 11 TRUE
8D 12 2 12 12 TRUE 12
TRUE


Hopefully this is correct, even tho its a bit slow in coming.

[davis_greatest]

Round 175 is still open, but...

Round 176 - Charlie gathers pace

And so, having gobbled bananas to his heart's content, Charlie, my pet chimpanzee, returns to continue the press conference. "Another interesting thing," he explains, "is that for the Belgian Apen, the players were divided into 8 equal groups, and the total number of points scored by each group was exactly the same!"

"Also," he goes on. "It was the first time we had introduced the new dress code, with bow ties being voluntary. In fact, only Barry the Baboon, Gordon the Gorilla, Oliver the orang-utan and I wore them!”

"Also," he continues, "some of the bow ties worn during the Apen were shaped like squares! And I just discovered that if you add up the squares of the number of points scored during the tournament by each ape wearing a square bow tie, you get almost exactly the same number as the total number of points scored (by all apes combined) during the whole tournament!"

"Almost exactly?" asks Lois Lane. "So not identical! How close?"

"Well, put it this way," says Charlie. "It could have been exactly the same, had just one ape without a bow tie potted just one more ball during the tournament."

"Which ball?" asks Lois. So Charlie, enjoying the limelight, shows a ball to the gathered press officers.

"That's interesting," Lois exclaims, being no slouch at logic. "So now I know how many apes wore square bow ties!"


What was the colour of the ball that Charlie displayed?

First in to name the colour correctly was snookersfun! Congratulations! The round is still open though!...

[davis_greatest]

Surely if they cannot pot a ball, then they cannot score a point!

Among other statements, Monique / Charlie said "Also one of the centuries's score was equal to..." so there had to be at least one century there!

[Lee Vilenski]

Well" said Charlie "None of the opponents of the 'century' players were able to pot a single ball!".

Surely if they cannot pot a ball, then they cannot score a point!

[davis_greatest]

Is it just nothing..... at alll.

No... how could at least one century be worth no points at all?

[Lee Vilenski]

hmmm

I didn't spot any TSF member at the Belgian Open but Charlie was there definitely! When I saw (or better heard) him he was helding a press conference in front of a bunch of journalists (the cheeky chimp!).
The guy from TheMoon just asked "What was the total number of points scored in this tournament's centuries?"
"It was actually remarkable!" answered Charlie " There was a square number of centuries, performed by a square number of players, each of them achieveing a square number of centuries! Even better, all centuries got a different score and these scores formed a suite of consecutive numbers. The lower and the higher centuries were actually "monochromatic" (15 reds + 15 times the same colour) total clearances. Also one of the centuries's score was equal to twice the number of centuries times the number of 'century' players". Needless to say, the guys looked nonplussed...
"Yes but..." insisted the repesentative of ZooComics "What was the total number of points scored in this tournament's centuries?"
"Well" said Charlie "None of the opponents of the 'century' players were able to pot a single ball!".
"Great" said the guy from WorldOfTheNews, in a high pinched voice, "but what was the total number of points scored in this tournament's centuries?"
Too late ... Charlie was gone. A fresh load of bananas was served at the buffet...

Well, finally, what was the total number of points scored in the Belgian Open's centuries?"

Charlie appears courtesy of D_G. Thanks!

Is it just nothing..... at alll.

[davis_greatest]

Round 175 is still open, but...

Round 176 - Charlie gathers pace

And so, having gobbled bananas to his heart's content, Charlie, my pet chimpanzee, returns to continue the press conference. "Another interesting thing," he explains, "is that for the Belgian Apen, the players were divided into 8 equal groups, and the total number of points scored by each group was exactly the same!"

"Also," he goes on. "It was the first time we had introduced the new dress code, with bow ties being voluntary. In fact, only Barry the Baboon, Gordon the Gorilla, Oliver the orang-utan and I wore them!”

"Also," he continues, "some of the bow ties worn during the Apen were shaped like squares! And I just discovered that if you add up the squares of the number of points scored during the tournament by each ape wearing a square bow tie, you get almost exactly the same number as the total number of points scored (by all apes combined) during the whole tournament!"

"Almost exactly?" asks Lois Lane. "So not identical! How close?"

"Well, put it this way," says Charlie. "It could have been exactly the same, had just one ape without a bow tie potted just one more ball during the tournament."

"Which ball?" asks Lois. So Charlie, enjoying the limelight, shows a ball to the gathered press officers.

"That's interesting," Lois exclaims, being no slouch at logic. "So now I know how many apes wore square bow ties!"


What was the colour of the ball that Charlie displayed?

[Monique]

And D_G also. Congratulations
It remains open ... it's pretty straightforward