Is your family like this?

Discrete Mathematics Level 2

4 brothers are told to stand in a row for their family portrait. Their heights are:

  • Abe: 4'6''
  • Ben: 4'
  • Clark: 3'6''
  • Dan: 3'

There's also a "Happy Birthday Dad!" poster that has to be held by 2 brothers standing next to each other, and in order to hold it straight, those two brothers have to be at most 6'' apart in height.

Mom's a bit crazy and wants to take a bunch of pictures so she has her sons stand in all 4! possible orders (ABCD, DCBA, DCAB, ... etc.) In how many of the shots can the poster be held evenly?


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