Puzzles with numbers and things

[davis_greatest]

Round 206 - More triangles!

A quick and easyish one, which I'm sure won't trouble the "experts".

My pet chimpanzee, whose name you all know by now, was marking out his new snooker table. He drew the baulk line, the spots, and the D.

He then drew on the baize, between the pink and black spots, a triangle - each side of which is equal to five balls' width.

He then places reds on the table - as many as he can - making sure that the centre (i.e. very bottom) of each red does not lie outside the triangle.

How many reds can he place on the table?

Answers initially by pager / PM please

[davis_greatest]

Round 205 closed

Congratulations snookersfun (by pager) and Monique!!!

The greatest possible number of kisses for round 205 is 2538, which you get if you put the 6 most affectionate gorillas in a group with the 4 most affectionate orang-utans, and the remaining 10 apes in the other group.

[Monique]

Indeed ... 2538 by having (13+10+10+8+7+6)*(15+11+9+7) +( 5+4+4+2)*(5+5+3+3+2+1)

[davis_greatest]

What about 2529? (13+10+10+8+7)*(15+11+9+7+5) + (6+5+4+4+2)*(4+3+3+2+1)
I got the previous answer by mistake ... (Clarissa went from 1 to 10, not from 4 to 10). Is there a cure to distraction?

2529 is even better - very good!

It can still be beaten though...

[Monique]

R205 ?

What about 2529? (13+10+10+8+7)*(15+11+9+7+5) + (6+5+4+4+2)*(4+3+3+2+1)
I got the previous answer by mistake ... (Clarissa went from 1 to 10, not from 4 to 10). Is there a cure to distraction?

[davis_greatest]

2490 kisses?

Not bad at all! How do you get 2490?

Higher is possible, though!

[Monique]

R205 ?

2490 kisses?

[davis_greatest]

Congratulations, snookersfun, for round 202!!! Wasn't that fun?

Not the only possible solution, but a perfectly valid one. Well done.

[snookersfun]

oooooooooh, there!!!!
well, that helped finally, attached is the a bit untidy pic (showing in white what I had accomplished before that tip and in yellow the continuation

I just hope it works... can't get my head to check this darn puzzle again now

[davis_greatest]

Round 202 clue

There seems to be a feeling that round 202 is difficult... so Charlie, in a fit of sympathy, has shown you below where to start.

As a reminder, you need to trace out the colours of the balls that Gordon potted in making 3 total clearances, moving along the squares horizontally, vertically or diagonally. Whenever Gordon potted a colour after a red, it was always worth 1 point more than the previous colour he had potted, except of course if the previous colour had been a black.

Round 205 is also open for anyone to post on the thread (solved by snookersfun).

[davis_greatest]

R200 answer

Well done D_G, abextra and snookersfun Would anyone please put the answer - with explanation - on the thread? Thanks!

How long did the tournament last? 31 days
How many matches were played every day? 15
Barry The Baboon came to watch on the first and last day: how many different players did he see in action? 11

There are 31 players. Each day consists of a league of 6 players, each of whom plays the other 5 players in his league that day. Since each match consists of 2 players, the number of matches in each league is 6 x 5 / 2 = 15.

Each pair of leagues has one player in common. So any two leagues consists of 2 x 6 - 1 = 11 players.

Each of the 31 players must play the other 30 players during the tournament - since he each plays 5 every day, each player plays on 6 days (5x6 = 30).

The total number of pairings must be 31 x 30 / 2 = 31 x 15. This is the same as the number of matches - 31 days of 15 matches each day.

[Monique]

R200 closing

Well done D_G, abextra and snookersfun Would anyone please put the answer - with explanation - on the thread? Thanks!

[davis_greatest]

...and snookersfun has answered round 205 correctly... ! Anyone else?

[davis_greatest]

Oh, you're answering round 205, chasmmi. I think you're getting your orangs and gorillas confused. Clarissa is a gorilla!

[davis_greatest]

So why is this not just:

So 6,7,8,10,13 pointer gorillas with 7,9,10,11,15 pointers orangs = 2288 kisses
1,2,4,4,5 gorillas with ,2,3,3,4,5 orangs = 272 kisses

= 2560

which round are you answering, chasmmi?