How to Get Away with Candy Hoarding
There are 9 houses in Spookytown which gives out candies to children for Trick or Treat. Each house gives a distinct number of candies, such that the number of candies the houses give form a consecutive progression. That is, if one house gives 42 candies, another gives 43, and so on.
Four children, Wes, Michaela, Laurel, and Connor went to ask for candies at this village. Each went to four houses. Surprisingly, each of the children went and asked for candies in such fashion:
No two children went to the same four houses.
No child went to a house that gave candies whose number was 1 more or 1 less to the house that gave them before.
No house gave out candies more than twice.
Meanwhile, Asher the bully was waiting for these kids to get their candies so that he could hoard them all. Wes, having the most candies, received 112. If the house giving the most and the house giving the second least number of candies were only visited once, how many candies will Asher have all in all?