paper-squares

hello,

 

Anna, Bea, Clara and Dana have many paper squares of the same size in the colours red, green, blue and white.

 

a) Each of the girls chooses one of the colours first; each chooses a different one.

Find out how many choices the girls have.

 

Now the girls cut all the paper squares along a diagonal into two triangles each.

They now make squares out of two of the coloured triangles.

 

b) How many different squares can the girls make this way?

How many of the squares are two-coloured? (definition of "two-coloured" : have two different colours)

 

c) Dana's little brother comes and wants to take two of the two-coloured squares.

How many ways are there to choose these two squares?

 

Note: Squares are considered equal if they fall apart due to rotations and shifts.

 

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Yes I know the solution of b) and c), but asinus made me uncertain with a):

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asinus said: The task is: Each of the girls first chooses one of the colours red, green, blue and white. Each girl chooses a different colour.

So for a) there are:

4 + 3 + 2 + 1 = 10 possibilities
 

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And I think there are 24 solutions (that's what I said:)

 

I said: There are actually 24 possibilities because of 4 factorial (4 * 3 * 2 * 1 = 24).

Again to check: Red = r., Blue = b., Green = g., White = w.:

rbgw

rbwg

rgbw

rgwb

rwbg

rwgb

brgw

brwg

bgrw

bgwr

bwrg

bwgr

grbw

grwb

gbrw

gbwr

gwrb

gwbr

wrbg

wrgb

wbrg

wbgr

wgrb

wgbr.

Finally, these are 24 possibilities for a).

 

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asinus said:

 

But you only have to add up the individual possibilities of each of the girls, multiplying afterwards would be wrong.

 

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Can someone actually come up with a correct, logical solution?

 

Maybe I shouldn't put this in the forum, but I just wanted to hear what you would say.

 

Straight