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September 10th, 2009, 11:46 PM   #1
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problem solving

there are 30 students in a class. they sit a 15 double desks, each ine is for two students. half of the girls sit with boys. is it possible to make a rearrangement so that half of the boys sit with girls.

thnx a gazillion
jc.xd

PS: can you show working out/reason thnx
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September 11th, 2009, 03:53 PM   #2
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Re: problem solving

Quote:
Originally Posted by jc.xd
there are 30 students in a class. they sit a 15 double desks, each ine is for two students. half of the girls sit with boys. is it possible to make a rearrangement so that half of the boys sit with girls.

thnx a gazillion
jc.xd

PS: can you show working out/reason thnx
It depends on the numbers of boys and girls.

Case 1: 14 girls and 16 boys. 8 boys sit with girls, 6 girls paired together, 8 boys paired together.
Case 2: 4 girls and 26 boys. There are not enough girls to pair off with 13 boys.

In other words there have to be at least 10 girls for boys to pair off, and at least 10 boys for girls to pair off.
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