let x be the value such that the sum of the numbers of the houses preceding the house number x is equal to the sum of numbers following it
⇒sum of preceding x=sum of following x
1+2+3.....+(x-1)=(x+1)+(x+2).....+49
⇒(x-1)/2*(1+x-1)=(49-x)/2*(x+1+49)
(x-1)/x=(49-x)(x+50)
x^2-x=49x+2540-x^2-50x
x^2-x=2540-x^2-x
2x^2=2540
x^2=1125
x=35
therefore value of x=35
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