Puzzles with numbers and things

[davis_greatest]

I'll just put the simple ones up, quite sure they can be bettered:

R263- 272
R264- 298

Very nice opening bids. And yes, they can be bettered.

Meanwhile, Monique has also solved R262. Congratulations

[davis_greatest]

... and abextra also has answered R162!

Next answers on the thread please. And if none by noon BST tomorrow, then explanations please on the thread from those who have answered it.

[dantuck_7]

R262 - The break as calculated by Rupert always comes out at 9.

The tricky bit is to proove it is always 9?!

[Monique]

That's not too difficult!

2*3*4*5*6*7=5040 a multiple of 9
this will multiply any score achieved when reds are exhausted. So the final score will always be a multiple of 9 with sum of digits (recurrently) equals to 0 mod 9 (this is the basis of the "trick" all kids learn at school to check divisibility by 9)

[davis_greatest]

Thanks Monique. I.e. the final score will always be a multiple of 9 (potting the green for 3 points and then pink for 6 points ensures this) and if you add the digits of any number divisible by 9, you get another number divisible by 9. Keep doing this, and the numbers will get progressively smaller, until you are left with 9.

[davis_greatest]

there are 73 games per match day and 146 match days needed one ball per match gives you 10658 balls in total if a ball is given in the final (you didnt state) makes 10659 balls in the triangle this equates to 145 rows in a perfect triangle and 74 balls left over in a back row 73 if one not in final so only you go away unhappy other than me trying to square root 81316 without a calculator

Cool... you're answering question 1 on the thread?

Edit: oh, you've deleted your post! Now I'm not sure what to do!

[Morse]

i deleted it cos i realised what i did lmao

[davis_greatest]

i deleted it cos i realised what i did lmao

LOL. Well, feel free of course to answer any of the earlier ones... just include a link to the post where the question was. For a few seconds, I had wondered what you were talking about!

[PaulTheSoave]

haha. lovely one this one was. I wonder how many days it took morse to answer!

[Morse]

not long about 15 mins after an unsuccessful search for a calculator first time i looked on this thread hence the dumb mistake lol however i could make it more difficult for you ?
the same question with a few more bits added on

[davis_greatest]

Back to question 1 then ()... as noted by Robert (post 2), there are 146+145+144+...+1 matches, and therefore the same number of red balls in the triangle.

You don't need to add this up to answer the question, as you can see that this gives a triangle of 146 rows. If you did add them up, you'd get 147 x 146 / 2 * = 10,731 balls.


* since each of the 147 players plays 146 other players, and we divide by 2 since each match consists of 2 players

[davis_greatest]

10658 balls because there are not 147 matches only 146 you dont play yourself !!!! so 73 per match day 146 match days thats why its an imperfect triangle

I know you don't play yourself. But each of the 147 players plays the other 146... hence 147 x 146 / 2 = 10,731.

Looking at it another way, place all 147 players in a line, one in front of another.

There are 146 players behind the person at the front, 145 behind the next person, 144 behind the next, .... and 1 behind the penultimate person.

So it is 146 + 145 + 144 + ... + 2 + 1, which also gives (of course) 10,731. This gives an equilateral triangle with 146 rows.

[Morse]

just got it you still have a week where you have the bye doh i knew it was easier than i was making it

[Morse]

and stop replying so quick i dont get chance to delete my mistakes go have lunch or something

[Morse]

equilateral why?

and why equilateral that just depends on the frame .... now i Know i am right with that one could be isosoles or scalene !