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Problem of the Week 798:

Overlapping Nickels

You are given a rectangular table and 1024 identical coins on it such that (a) no 2 coins are touching, (b) no coin touches the edge of the table.

Try to place as many coins as you can on the table with a new set of rules where you are allowed to overlap coins and touch the edge of the table, but (i) all coins must have their centers inside the table and (ii) their centers are not covered by any other coin. (The second arrangement can be independent of the first.)

The person with the largest answer wins.

© Copyright 1996 Stan Wagon. Reproduced with permission.

The Math Forum

2 October 1998