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Melody

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यूजर का नामMelody
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WELCOME BACK CPHILL !


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Melody  11 Feb 2022
 #1
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Hi Jedithious, it is great to see you back again.


"In how many different ways can you arrange 2 blue blocks and 2 red blocks in a straight line?"

I believe the answer is 4P4 / ( 2P2 * 2P2)

there is a nPr button on your calculator or

nPr = n! / (n-r)!
so 4P4 = 4! = 2 x 3 x 4 = 24 Thats how many ways 4 different coloured blocks can be arranged in line.
Then you have to divide by
2P2 because there are 2 red ones 2P2 = 2! / 0! = 2
and you have to divide by 2P2 again because there are 2 red blocks 2P2=2

So I think the answer is 24 / (2*2) = 6

These are the possible permutations RRBB,RBRB,RBBR,BRRB,BRBR,BBRR THAT IS IT!
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Now, lets look at how many ways you can order 4 different books in a more straight forward way.
There are 4 ways to choose the first book
now there are 3 books because there is one on the shelf already.
so there are 3 ways to choose the 2nd book
there are 2 ways to choose the 3rd book and
there is only 1 book left so there is only one way to choose it.
So, there are 4*3*2*1 ways of ordering the 4 books
this is 4!, it is also 4P4.
The P stands for permutations.
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Now you can do the other 2 by yourself I think
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You might find this interesting.
http://www.mathsisfun.com/combinatorics/combinations-permutations.html
28 Jan 2014
 #24
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Thankyou for this wonderful letter Michelle,

I would like to do it justice with a proper reply but I don't think that I have enough time right now.
There are a few things that I can say straight away.

I just watched the water leave two of my sinks. Both times the water spun clockwise. Yes, I too had heard it spins in a different direction in the north a and south hemisphere. This is something one of us should google properly.

Zamarronics is one of our guests. If you look back over the earlier pages of this post you will see what it is all about. The maths was quite impressive. Zamarronics came up with a
formula and it is me that called the Zamarronics formula. So I am not surprised that you couldn't find it when you googled.

I'd like to play with the factorial idea as well. DavidQD (and my other friends) did a great job on Walt's one. Maybe we could turn it into another puzzle thread. I wish I had more time but I guess that is the case with most people in life.
I was much more active with the puzzles when school was on holidays. It is difficult now as the 'proper' questions should take priority i guess. Australia hasn't gone back to school yet plus I think more people are finding the forum all the time so it might get even busier. I do want to leave time for games and number puzzles etc. This is important to me too.

Your basic level divisibility checks were all correct I believe.

I haven't looked at what you did with the higer level factorising yet, sorry.

That's it for now I think.
Melody.
27 Jan 2014