The houses of a row are numbered from 1 to 49. Show that there is a value of `x` such that the sum of the numbers of the houses preceding the house numbered `x` is equal to the sum

Explanation

Here, we are given
`S_(x-1) = S_49 - S_(x-1)-x`

`2S_(x-1)+x = S_49->(1)`

Here, `S_(x-1)` is the sum of first (x-1) natural numbers.
`:. S_(x-1) = ((x-1)(x-1+1))/2 = (x(x-1))/2`

`S_49` is sum of first 49 natural numbers.

`:. S_49 = (49**50)/2 `

Putting these calues in (1),
...