Filling the Hilbert Hotel with the high school band kids on an infinite number of infinitely large school buses....

Andy Long, Spring 2024

You’re on bus b, seat number s; you finally get to the counter, and are told to go to which room?

Clear[b,s]

roomNumber[b_,s_]=Simplify[Together[(s+b)(s+b-1)/2-(b-1)]]

diags=5;
roomNumberName=Table[StringJoin["Rm",ToString[i]],{i,1,diags*(diags+1)/2}];
busName=Table[StringJoin["Bus",ToString[i]],{i,1,diags}];
seatName=Table[StringJoin["Seat",ToString[i]],{i,1,diags}];

data=Table[Table[{0,roomNumber[b,s]},{s,1,diags-b+1}],{b,1,diags}];
Flatten[data,1];
p1=ListPlot[
data,PlotMarkers->busName
];

data=Table[{b,s},{b,1,diags},{s,1,diags-b+1}]
p2=Show[
ListPlot[data,PlotMarkers->busName,Axes->True,AxesOrigin->{0,0}]
(* Graphics[Text["(1,1)",{1,1}]]*)
];

GraphicsGrid[{{p2,p1}}]