[lgaimari]

Please don't think this ridiculous, but I need to know how many 18" balloons I need to cover a ceiling that measures 70' x 21'.

Please help me! I'm a 42 year old woman who was recruited to the prom committee at my school and I have no idea how many balloons to order!

[ebaines]

Actually this kind of question in not so straight-forward, so don't feel bad asking! I can give you a range, as the actual number needed depends on how you position the balloons against the ceiling. If you stick them to the ceiling in nice neat rows and columns - so that each balloon has a neighbor to the left, one to the right, one in front, and one behind (4 around 1 arrangement) - you'll be able to fit 46 rows along the 70' dimension, and 14 columns along the 21' dimension, for a total of 46*14 = 644 balloons. However, if instead you pack the balloons as tightly as possible, you'll find that a "6 around 1" packing arragement is optimal, and in this case you can get about 756 balloons packed in. All of this assumes that the balloons are to be packed exactly 1 layer (no overlapping balloons).