Ok, one more coin question (for now). This one might be tricky, we'll see. The solution is very elegant.
You have 100 perfectly round and identical quarters on a rectangular table arranged such that none of them overlap (ie. all quarters are flat on the table) and it is impossible to add another quarter to the table without requiring an overlap.
Show that you can always cover the table completely with 400 coins (where, by "cover", I mean that for every point on the table, there is at least one coin directly above it). Obviously, the covering would allow for overlaps.
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