Puzzles with numbers and things

[snookersfun]

nah, he didn't want to do my ironing either...
maybe, you'll ask him for me...

[April madness]

Snookersfun, I am sure if you ask DG very nicely he'll award you points too

[snookersfun]

Perhaps I'll award you 10 points if you ask very nicely.

that'll be the day I stop breaking my head to answer questions on this thread

and you think playing with matchsticks and lemons would have been faster-lol







seriously though- impressive

[davis_greatest]

Only if you award me at least 19

Perhaps I'll award you 10 points if you ask very nicely.

[davis_greatest]

OK, when I originally explained this on the BBC site (I made the question a bit easier then), I did it with matchsticks and lemons. So I'll use matchsticks and lemons again...

Suppose first of all that there were a ball available of every possible value from 1 to 12 (rather than just 1,2,3,4,5,6,8,10 and 12) - then let's count how many ways.

You can do this by representing every sequence using 12 lemons (0), with some matchsticks (!) separating them to correspond to the value of each ball potted.

For example, blue-black (5-7) would be represented by 5 lemons, matchstick, 7 lemons, as follows:

0 0 0 0 0 ! 0 0 0 0 0 0 0

12 reds would be shown as lemon, matchstick, lemon, matchstick, lemon, matchstick, lemon, matchstick, lemon, matchstick, lemon, matchstick, lemon, matchstick, lemon, matchstick, lemon, matchstick, lemon, matchstick, lemon, matchstick, lemon:

0 ! 0 ! 0 ! 0 ! 0 ! 0 ! 0 ! 0 ! 0 ! 0 ! 0 ! 0

So the number of sequences is just the number of ways of putting or not putting a matchstick in each of the 11 gaps between lemons, i.e.

2^11 = 2048 ways.

Now remember that in Snooker Plus there are no balls worth 12, 11 or 9 points, so some of the ways are impossible. These are:

a) using a 12-ball ------------------> 1 way
b) using an 11-ball -----------------> 2 ways (11-1 or 1-11)
c) using a 9-ball:
(i) with a 3-ball -------------------> 2 ways (9-3 or 3-9)
(ii) with a 2-ball and a 1-ball -------> 3! = 6 ways (1-2-9 or 1-9-2 or 2-1-9 or 2-9-1 or 9-1-2 or 9-2-1)
(iii) with three 1-balls --------------> 4 ways (9-1-1-1 or 1-9-1-1 or 1-1-9-1 or 1-1-1-9)

Total impossible ways: 1+2+2+6+4 = 15

So we need to deduct 15 ways from 2048, and arrive at 2033.

PS I wanted to use as lemons, but I am not allowed to use more than 4 smileys in a message, apparently!

[snookersfun]

Wow! That must have taken you a while?!

I'll post my way in a short while.

less than 1 h , with quite a lot of work related disturbances as well

I am sure there exists a formula to reach a certain value from possible types of values. e.g. use all the values for 1-10 to reach 12 and just substract the possibilities including 9 (which is really only missing). Just would have taken me longer to find this formula, I would think.

[April madness]

You think THAT'S unfair? Wait till you see me award myself 20 points!

Only if you award me at least 19

[davis_greatest]

Wow! That must have taken you a while?!

I'll post my way in a short while.

[snookersfun]

Just when I thought, I am exempt from giving explanations.
wrote them all up.... lol


No, well wrote up all the possible kind of combinations
e.g. 10,2;
10,1,1;
8,3,1
8,2,2,
8,2,1,1, etc. you get the drift

and then calculated for each of these the possible permutations,
actually using the formula for possible permutations:
# of rearrangements for n numbers, k1,k2,...kn, types:
= n!/(k1!k2!...kn!)

and then made 100 possible mistakes in adding them all up...

I am sure, you'll have a shorter way, let me know, would love to learn!

[davis_greatest]

well, well, so I did get it right in the end. Rather encouraging. I had to correct about 5, 6 minor calculation mistakes though... could get quite embarrasing to post so many wrong answers.
anyway, have to sit some out in the future, as workload will defo increase quite soon

How did you get your answer of 2033?

[davis_greatest]

Double standards!



Just kidding

You think THAT'S unfair? Wait till you see me award myself 20 points!

[snookersfun]

well, well, so I did get it right in the end. Rather encouraging. I had to correct about 5, 6 minor calculation mistakes though... could get quite embarrasing to post so many wrong answers.
anyway, have to sit some out in the future, as workload will defo increase quite soon

[April madness]

This is my 200th post - I am going to turn yellow!

I've noticed that editing of posts can sometimes make it difficult to see who answered first, or what a previous answer was etc. There will therefore be a new rule on this thread - for future questions, once an answer has been given, that post may not be edited, or it will be disqualified - in the same way as for The Statman's prediction competition. If you wish to change or clarify your answer, please paste it and amend it in a new post.

Of course, that rule does not apply to me, if I need to clarify the wording of a question!

Double standards!



Just kidding

[davis_greatest]

New rule - no editing!

This is my 200th post - I am going to turn yellow!

I've noticed that editing of posts can sometimes make it difficult to see who answered first, or what a previous answer was etc. There will therefore be a new rule on this thread - for future questions, once an answer has been given, that post may not be edited, or it will be disqualified - in the same way as for The Statman's prediction competition. If you wish to change or clarify your answer, please paste it and amend it in a new post.

Of course, that rule does not apply to me, if I need to clarify the wording of a question!

[davis_greatest]

Next round to follow tonight

I have to do some work now! I will try to post a question on colourful socks tonight.