>2 slices of bread ontop of eachother with a filling between them is considered a sandwich (basic definition I know)>by this metric a slice of bread with a filling between it and the slice of bread ontop of it that also has a filling between it and the slice of bread ontop of it (3 slices of bread with filling in every gap) would be 3 sandwiches >1 sandwich between the top and middle slice of bread, another between the top and bottom slice of bread (the filling is both the meat and the middle slice of bread) and the other being between the middle and bottom slice of bread >for 10 slices of bread (all with filler) there would be 9 (traditional sense) + 8 (from the sandwich set of the top slice and -1 for the traditional sandwich already counted) + 7 (from the second slice down onwards again -1 from the traditional set) + 6 + 5 + 4 + 3 + 2 + 1 (same rule) = 45 sandwiches >if I have 2 slices of bread (with filler) standing upright between 2 slices of bread horizontally I have 2 sandwiches with the first being the traditional sandwiche and the second being the bread between the horizontal slices of bread Going by these rules is there any theorem that can be applied to the following question>assuming each slice of bread is 5cm and each filling is 0cm what arrangement will allow me to fit the most amount of sandwiches in a 1 cubic meter roomAnd if so can it be altered and applied to this question >assuming the same measurements what would be the most optimal arrangement in the scenario where the filling also becomes 5cm I know it sounds really retarded but I never got to finish my math course in college and I really want to know if theres a way
I forgot to give width and thicknessWidth 5cm Thickness 2cm Both bread and filling
>>16478222I can't tell if you're trying to get people to help you with your homework in a convoluted way, you're schizophrenic or you're just really into sandwiches.
>>16478285I'm really into sandwiches anon I first got the idea by asking what is a sandwich (I got up to the point where pie could technically be considered a sandwich) Then I realized you could calculate how many sandwiches are in a stack of bread by doing n!-1 where N is the amount of slices of bread stacked ontop of eachother Then I started to consider the classic queen of how many of x can you fit in y And from there I realized because of the rules for sandwiches it might look a little different then just boring rows of stacked bread especially because the filling can just be more bread I also now just realised that if you take cocktail sticks and attach slices of bread together in a wheel you have an infinite number of sandwiches because each slice of bread is sandwiched between another slice of bread which is sandwiched between another and so onBut yeah I'm just sort of wondering if there is a formula for this kind of geometry
>>16478222What the fuck is this picture
>>16478307You should look into tiling problems. You could probably find an optimal tiling solver that could solve it numerically, and if you're lucky it might be something that there's a closed form solution for. Convex spaces tend to be good for that.
