Puzzles with numbers and things

[davis_greatest]

Round 356 - Triangular bananas

Charlie has asked you to come along with him to buy some snooker balls from Barry The Baboon’s Ball Shop. Charlie would like to buy 15 balls to place in his triangle to set up for a new game of Snookchimp, but the balls don’t need to be all reds. In fact, Charlie wants to set up the balls so that no balls of the same colour touch each other. (Imagine the balls are touching in the picture below, as they should be once set up!)

The balls that Charlie can choose are red, yellow, green, brown, blue, pink or black (so red is a “colour” here), all with their usual snooker values (1 to 7) – as many as he likes of each, as long as he has 15 in total.

Barry tells Charlie that Charlie will have to pay for the balls in bananas, with the cost determined as follows. Once Charlie has set up the balls in the triangle, Barry will look at the total points value of each of the 5 rows and find the biggest difference he can between adjacent rows. That difference will be the number of bananas that Charlie has to pay.

For example, if Charlie sets out the balls as shown, the value of the rows would be 2, 11, 14, 11 and 19 points. The biggest difference between adjacent rows would be 9 (the difference between the first two rows of 2 and 11), so Charlie would have to pay 9 bananas.

Also, once Charlie has laid out the balls, Barry is allowed to rotate the triangle however he likes before determining the banana cost! Barry will always try to get as many bananas as he can. For example, if Barry rotated the triangle below by 120 degrees clockwise, the rows would be 4, 3, 12, 17, 21 – but that would still give 9 bananas (the difference between 3 and 12).

Note the picture below is an example only, and you and Charlie can choose different coloured balls. There is also a blank pack in case anyone wants to colour it.

Help Charlie determine which balls to buy and how to arrange them, to make the cost as cheap as possible.

Please bid here on the thread the cheapest banana cost you find. Once we have a nice bid (or bids), you will be asked to show the balls chosen.

[abextra]

Round 355 - lol, I found the same way as Snookersfun (148 points with the 15 reds), and didn't check the final colours... just copied the 43 points from R354...

[davis_greatest]

Round 354 - not sure at all - hope it works:

black into black , pink into green , brown into brown ,
black into black , pink into green , brown into brown ,
black into black , green into green , blue into blue , pink into pink , yellow into yellow ,
black into black , green into green , blue into blue , pink into pink ,

yellow into yellow , green into green , brown into brown , blue into black , pink into brown , black into black

Congratulations, abextra - another maximum! Also worth a bit of extra credit for being easier to check, as it was very close to the one I had!

[davis_greatest]

I hope these hold, but will put it up invisible for now for those still trying their luck

Yes, congratulations, snookersfun. Now I have remembered the rules and checked them, they are both correct and each is a "maximum". :snooker:

[abextra]

Round 354 - not sure at all - hope it works:

black into black , pink into green , brown into brown ,
black into black , pink into green , brown into brown ,
black into black , green into green , blue into blue , pink into pink , yellow into yellow ,
black into black , green into green , blue into blue , pink into pink ,

yellow into yellow , green into green , brown into brown , blue into black , pink into brown , black into black

[davis_greatest]

R354, I'm going to stick with 200.
Pink into pink, blue into yellow, black into black, green into green, brown into brown, black into black, green into green, brown into brown, black into black,
green into green, brown into brown, black into black, green into green, blue into blue, pink into pink...... yellow into yellow, green into green brown into brown, blue into yellow, pink into pink, and black into blue.

Too to go on....

Congratulations, moglet - a very good break of 200! :snooker: Just two less than the 202 maximum possible.

[abextra]

Lol - I got lost in these new rules too. I'm glad you joined me.

[snookersfun]

Ehh... what's wrong with yellow pocket after pink pocket?

he managed to confuse himself this time

[davis_greatest]

Ehh... what's wrong with yellow pocket after pink pocket?

Nothing - sorry - am trying to check these while asleep and I can't remember how the game works.

[abextra]

Ehh... what's wrong with yellow pocket after pink pocket?

[snookersfun]

WOW, Snookersfun, you're a genius!!! Very well done! :snooker:

Thank you! Although, must admit the first one was more a matter of luck.
Are they good then?

[davis_greatest]

WOW, Snookersfun, you're a genius!!! Very well done! :snooker:

snookersfun, I think you have an illegal pot into a yellow pocket after a pink pocket in round 354? EDIT - was too sleepy to remember the rules - ignore this, sorry - not illegal pot at all.

Checking the others now.

abextra, how about yours?

[abextra]

I hope these hold, but will put it up invisible for now for those still trying their luck
....207

WOW, Snookersfun, you're a genius!!! Very well done! :snooker:

[snookersfun]

I hope these hold, but will put it up invisible for now for those still trying their luck
R. 354: black-black... 14
green-green.....6
blue-blue.......10
pink-pink........12
yellow-yellow...4
black-black.....14
brown-brown....8
pink-yellow.......6
black-black.....14
brown-brown....8
pink-yellow.......6
black-black.....14
green-green.....6
blue-blue........10
pink-pink........12
_______________
..................144
15 reds..........15

yellow-yellow...4
green-green.....6
brown-brown....8
blue-black........5
pink-brown.......6
black-black.....14
________________
.....................43
________________
.....................202

and R. 355:
black-black... 14
green-green.....6
pink-pink........12
blue-blue.......10
black-green.....7
pink-pink........12
blue-blue.......10
black-green.....7
pink-pink........12
blue-blue.......10
black-green.....7
pink-pink........12
blue-blue.......10
black-green.....7
pink-pink........12
_______________
..................148
15 reds..........15

yellow-yellow...4
green-green.....6
brown-pink.......4
blue-blue........10
pink-green........6
black-black.....14
________________
.....................44
________________
.....................207

[moglet]

R354, I'm going to stick with 200.
Pink into pink, blue into yellow, black into black, green into green, brown into brown, black into black, green into green, brown into brown, black into black,
green into green, brown into brown, black into black, green into green, blue into blue, pink into pink...... yellow into yellow, green into green brown into brown, blue into yellow, pink into pink, and black into blue.

Too to go on....