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# Boys and girls circle

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40 boys and 28 girls stand in a circle, hand in hand, all facing inward. Exactly 18 boys give their right hand to a girl. How many boys give their left hand to a girl?

Mar 8, 2019

#10
+110093
+1

40 boys and 28 girls stand in a circle, hand in hand, all facing inward. Exactly 18 boys give their right hand to a girl. How many boys give their left hand to a girl?

If a boy gives his right hand to a girl then looking from the middle of the circle the girl is on the left.

So from the centre of the cirle the pairs look like    GB (clockwise)

So we have  18 pairs of   (GB)    these pairs must be kept together.         [What I need to determine is how many  BG there will be]

Now there are 22 boys and 10 girls not accounted for although it would actually make no difference at all how many more children that there were.These children can be slotted in anywhere in the circle SO LONG AS for each slot postion the boys go first and the girls go second ( BG clockwise). It does not matter how many boys or girls get slotted in between each pair as long as they all get slotted in.

Between each of the original  GB couples, who can be inbetween

GB                           nothing                           GB                BG will be together  (once)

GB                          all boys                            GB                BG will be to together once at end

GB                           all girls                            GB                 BG will be together once at the beginning

GB        some boys followed by some girls     GB                 BG will be together once in the middle.

So no matter where the extra kids are sloted in (so long as the boys first then girls after rule is followed) there will be exactly ONE BG combination between each of the original pairs. HENCE if there are exactly 18 GB combinations there will also be exactly 18 BG combinations.

i.e.

If exactly 18 boys give their right hand to a girl THEN exactly 18 boys will give their left hand to a girl.

Ther fact that there is 22 extra boys and 10 extra girls (above the 18 original pairs) is irrelevant.

CREDITS:

Tetre showed me this site:   https://answers.yahoo.com/question/index?qid=20150213031605AAcDi2g   (Thanks Tetre   )

Initially I had a real problem working out the logic but I think my answer is very similar to the second answer given.

Mar 10, 2019
edited by Melody  Mar 10, 2019

#1
+428
-5

I'm thinking subtract 18 from 40 would be a basic thing to do I'm just curious if this is like a trick question......

Mar 8, 2019
edited by HiylinLink  Mar 8, 2019
edited by HiylinLink  Mar 8, 2019
#2
+110093
0

That is a really tricky question.  I wonder if there really is just one answer???

Mar 8, 2019
#4
+110093
+2

40 boys and 28 girls stand in a circle, hand in hand, all facing inward.

Exactly 18 boys give their right hand to a girl. How many boys give their left hand to a girl?

If you had the   King at one 'end' of the the table with the Queen on his right    KQ

then you have all the maids to the right of the queen (there are 10 of them)      FFFFFFFFFF

then you have the married couples  with the wife always on the right. (17 of them )    MF MF MF MF MF MF MF MF MF MF MF MF MF MF MF MF MF

then you have all the bachellors with the king to the right of the last one    (   22 of them)   M .....    M

Which boys have girls on their left ?

Not the king

All 17 of the couples do

One of the bachelors does  (lucky him)

So that is 18.

It probably always works out to 18.

Melody  Mar 9, 2019
#6
+428
-1

I know right I mean I'm thinking its implicitly saying something.

#3
+4595
+1

Hint: 22 boys give their right hand to a boy.

I know, it's a hint, but it's pretty big, as you can get the answer from there.

Mar 9, 2019
#5
+110093
0

THANKS TERTRE

Tertre, I have written a more full answer.   (I started before you but finished after)

I could not get it from your hint.  EDIT : (Maybe I could, I have not thought about your hint very much yet)

Even what I have done is only one scenario.  I have not shown that it will always be the case.

I have not been able to get my head around the general case myself.

Anyway, I will leave mine hidden for a bit and see if the guest comes back and interacts with you.   :)

Melody  Mar 9, 2019
edited by Melody  Mar 9, 2019
edited by Melody  Mar 9, 2019
#7
0

Thank you for the hint. I am still a bit confused. I am guessing the answer is 40-22=18. Not sure about figuring out the 22 part. Is it a trick question or am I just not "getting it"?

Guest Mar 9, 2019
#8
0

My first attempts to reply wouldnot go through. I am trying to move one answer up in the list of responses.

My original response:

Thank you for the hint. I am still a bit confused. I am guessing the answer is 40-22=18. Not sure about figuring out the 22 part. Is it a trick question or am I just not "getting it"?

Guest Mar 9, 2019
#9
+4595
+1

Then, you are left with 18 boys with uncovered left hands, so they must be paired to hold the right hands of the girls.

tertre  Mar 10, 2019
#10
+110093
+1

40 boys and 28 girls stand in a circle, hand in hand, all facing inward. Exactly 18 boys give their right hand to a girl. How many boys give their left hand to a girl?

If a boy gives his right hand to a girl then looking from the middle of the circle the girl is on the left.

So from the centre of the cirle the pairs look like    GB (clockwise)

So we have  18 pairs of   (GB)    these pairs must be kept together.         [What I need to determine is how many  BG there will be]

Now there are 22 boys and 10 girls not accounted for although it would actually make no difference at all how many more children that there were.These children can be slotted in anywhere in the circle SO LONG AS for each slot postion the boys go first and the girls go second ( BG clockwise). It does not matter how many boys or girls get slotted in between each pair as long as they all get slotted in.

Between each of the original  GB couples, who can be inbetween

GB                           nothing                           GB                BG will be together  (once)

GB                          all boys                            GB                BG will be to together once at end

GB                           all girls                            GB                 BG will be together once at the beginning

GB        some boys followed by some girls     GB                 BG will be together once in the middle.

So no matter where the extra kids are sloted in (so long as the boys first then girls after rule is followed) there will be exactly ONE BG combination between each of the original pairs. HENCE if there are exactly 18 GB combinations there will also be exactly 18 BG combinations.

i.e.

If exactly 18 boys give their right hand to a girl THEN exactly 18 boys will give their left hand to a girl.

Ther fact that there is 22 extra boys and 10 extra girls (above the 18 original pairs) is irrelevant.

CREDITS:

Tetre showed me this site:   https://answers.yahoo.com/question/index?qid=20150213031605AAcDi2g   (Thanks Tetre   )

Initially I had a real problem working out the logic but I think my answer is very similar to the second answer given.

Melody Mar 10, 2019
edited by Melody  Mar 10, 2019