answers to yahoo question - maths prob

Maths Problem Help! 10 Points for right answer!?
36 people live in the eight houses in Albert Square.Each house has a different number of people living in it.Each line of three houses has 15 people living in it.How many people live in each house/It's basically a 3x3 grid with no house in the middle (Just a tree)How many in each house?!


let

row 1 h1(n1) h2(n2) h3(n4)

row 2 h8(n8) Tree h4(n5)

row3 h7(n7) h6(n6) h5(n5)

h1, h2 , h3, h4 , h5, h6, h7 , h8 be the 8 houses. Tree is in the centre,
ni,n2,n3,n4,n5,n6,n7,n8 are number of people accommodated in h1, h2 , h3, h4 , h5, h6, h7 , h8

36 people are to accommodated in the 8 houses with the condition,
n1+n2+n3 =15
n3+n4+n5 =15
n5+n6+n7= 15
n7+n8+n1=15

Soulution:

We will start with equal distribution in corners


9 0 9

0 tree 0

9 0 9

Now we will distribute the 9 in house h3 into h2, h3 , h4 equally


we will distribute the 9 in house h3 into h2, h3 , h4 equally.

we will distribute the 9 in house h7 into h6, h7, h8 equally



9 3 3

3 tree 3

3 3 9

It is not the only solution, number of solutions are possible

9 2 4
3 Tree 2
3 3 9


9 2 4
2 Tree 2
4 2 9



9 1 5
2 Tree 1
4 2 9



9 1 5
1 Tree 1
5 1 9

And so on….

S Ramakrishnan, oasisram@yahoo.com