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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