1

Part of 1996 Putnam

Problems(2)

Source:

Find the least number

A

such that for any two squares of combined area

1

, a rectangle of area

A

exists such that the two squares can be packed in the rectangle (without the interiors of the squares overlapping) . You may assume the sides of the squares will be parallel to the sides of the rectangle.

Putnamgeometryrectanglecollege contests

Source:

Define a \emph{selfish} set to be a set which has its own cardinality as its element. And a set is a \emph{minimal }\text{ selfish} set if none of its proper subsets are \emph{selfish}. Find with proof the number of

\text{minimal selfish}

\{1,2,\cdots ,n\}

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