TITLE: There are 31 houses on north street numbered from 1 to 57. Show at least two of them have consecutive numbers.
QUESTION [6 upvotes]: I thought to use the pigeon hole principle but besides that not sure how to solve.

REPLY [3 votes]: Not sure if this is the answer you were looking for, but it's one of those "so painfully simple that you likely never considered it":
North Street ends in a cul-de-sac.
But more to the point...
If houses are numbered 1 through 57 and NONE of them are consecutively numbered, they must all have odd numbers.  All odd numbers from 1 to 57 (inclusive) total 29 numbers.
The problem cites 31 houses in a range which can only accommodate 29 houses without any adjacent houses.  31-29 = 2, therefore at least two of the houses must be adjacent to others in order to fit within the parameters.
Even if the question cited 30 houses, at least two would have adjacent numbers.  For example, if the 30th house was numbered 2, houses 1, 2, and 3 would all have adjacent numbers.