Thread: help with problem solving question

there are 30 students in a class. they sit at 15 double desks, each one is for 2 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
justanotherperson

PS: can you also explain your answer

if b stands for boys and g for girls

notice that

b+g=30

also

b/2+g/2=15

if you say half of the girls (g/2) sit with boys this means g/2 is a pair number

but as b/2+g/2=15, b/2 cant be a pair number so its not possible.



edit:to explain better this

if you say half of the girls (g/2) sit with boys this means g/2 is a pair number

this is because g must be pair (cant cut people in half)
and as half of the girls sits with boys and other half sit together in groups of 2
g/2 people sit in groups of 2, so g/2 must be also pair