Puzzles with numbers and things

[davis_greatest]

Happy New Year to everyone!

http://cards.101newyear.com/cgi-bin/cards/showcard.pl?cardnum=ZCW81231133736265&log=ny101

Hehehehehehehehehehehehehe Happy new year!!!

[davis_greatest]

Round 97 - Chimpsnooker with fewer balls

Has still no one else had a go at snookersfun's round 96? Good luck with it!

Here is round 97 in the meantime. It might be the last round I post on this thread - at least for a while....


Round 97 - Chimpsnooker with fewer balls

Gordon is is about to break off in a frame of Chimpsnooker against Charlie . As you will recall, Chimpsnooker is played with a triangle of 20 rows of reds (that's 210 reds)! This time, the triangle has been set up the right way round!

However, Gordon looks at the table and agrees with Charlie that 20 rows of reds really is a bit too much. The frame will take all night. So, they agree to remove some reds, in order to leave a smaller equilateral triangle. The triangle can be of any size from one row to 19 rows. For example, it could have 5 rows (with a total of 15 reds) like normal snooker. If it has one row, that would mean (of course) just one red - so, there are 210 possible "one ball" triangles!

The triangle must be the right way round (i.e. the apex red must be towards the pink rather than the black). It does not matter if it is shifted left or right. Two possible smaller triangles are shown as examples below (one with 5 rows and one with just one row).

So.... how many possible triangles can be left for the game of Chimpsnooker with fewer balls?


PS On New Year's Eve, someone rated this thread one star (Terrible) - so, if the quality has deteriorated to such an extent, I shall refrain from posting further questions until either (a) that person gives the reasons on this thread for that rating (and preferably links to a better thread of his/her own) or (b) this thread's average rating gets back to its previous level.

[Snooker Rocks!]

There have been 11 votes, with a 4.36 average. I haven't voted this thread yet, so I shall do so now. Hopefully this will get the rating back to where it should be and davis_greatest can keep posting marvellous questions

As to Round 97, would the following triangles be counted as the same or different? They have the same dimentions but different reds have been removed:

--------------O--------------
-------------OO-------------
------------OOO------------
-----------OOOO-----------
----------OOOOO----------

and...

--------------O--------------
-------------OO-------------
------------OOO------------
-----------OOOO-----------
----------OOOOO----------

So are those triangles different or the same?

Actually I suppose they're the same because they have the same dimentions

Edit: I'm going to take an educated guess at the answer: 1435?

[snookersfun]

So.... how many possible triangles can be left for the game of Chimpsnooker with fewer balls?

wait, are we supposed to PM, I'll PM it now

PS On New Year's Eve, someone rated this thread one star (Terrible) - so, if the quality has deteriorated to such an extent, I shall refrain from posting further questions until either (a) that person gives the reasons on this thread for that rating (and preferably links to a better thread of his/her own) or (b) this thread's average rating gets back to its previous level.

some grinch we need two more 5 star votes!!!

and, let's add this as well: I will close my round tonight 6 pm GMT.

[davis_greatest]

There have been 11 votes, with a 4.36 average. I haven't voted this thread yet, so I shall do so now. Hopefully this will get the rating back to where it should be and davis_greatest can keep posting marvellous questions

As to Round 97, would the following triangles be counted as the same or different? They have the same dimentions but different reds have been removed:

--------------O--------------
-------------OO-------------
------------OOO------------
-----------OOOO-----------
----------OOOOO----------

and...

--------------O--------------
-------------OO-------------
------------OOO------------
-----------OOOO-----------
----------OOOOO----------

So are those triangles different or the same?

Actually I suppose they're the same because they have the same dimentions
Edit: I'm going to take an educated guess at the answer: 1435?

These triangles count as different because they are in different positions. (That's why there are 210 triangles of just one ball - although, they are all the same size, they are in different positions. )

1435... not bad, but that's not what I make it, I'm afraid.... Try another guess!

[austrian_girl]

Seems I have been the saviour of this thread. Never rated a thread before but I'm glad I could restore the well-deserved position of this one.

[snookersfun]

Seems I have been the saviour of this thread. Never rated a thread before but I'm glad I could restore the well-deserved position of this one.

Yay!! Now, that looks better. Hugs and thumbs-up to the three recent voters

[Snooker Rocks!]

I know you can work out the number of squares on a chess board by using the formula:

http://www.qubesite.co.uk/magicsite/...b39dee2223.png

So I thought 20 rows would just be:

http://www.qubesite.co.uk/magicsite/...698b07cd49.png

i.e. 1435

I'll make another guess, 1436?

[davis_greatest]

I know you can work out the number of squares on a chess board by using the formula:

http://www.qubesite.co.uk/magicsite/...b39dee2223.png

So I thought 20 rows would just be:

http://www.qubesite.co.uk/magicsite/...698b07cd49.png

i.e. 1435

I'll make another guess, 1436?

Hehehe... that's a chessboard with squares. This is a snooker table with triangles.

Here's a clue, Snooker Rocks! - this question is very similar indeed to one that you asked not long ago! At least, although it may sound different, it can be translated into a very similar problem.

[Ginger Freak]

I got to 1475 but then realised that I have probably made a mistake! (Unless I haven't?)

[davis_greatest]

I got to 1475 but then realised that I have probably made a mistake! (Unless I haven't?)

I've had one correct answer by PM - it's not 1475, sorry! It is possible to come up with a neat, simple formula - rather than by doing lots of counting (which is lucky, as I was in bed three-quarters asleep when I three-quarters dreamt my answer)! But whichever way suits you most.

[Ginger Freak]

Realised where I went wrong - 1540

[davis_greatest]

Realised where I went wrong - 1540

Very close! Re-read the question carefully.

[Ginger Freak]

Oh yes - 1330!

[snookersfun]

Oh yes - 1330!

ouch..... and I thought you are there, lol