41

Part of 1970 IMO Longlists

Problems(1)

There exists a point A on a cube - Nice one

Source: IMO LongList 1970 - P41

Let a cube of side

1

be given. Prove that there exists a point

A

S

of the cube such that every point of

S

can be joined to

A

S

of length not exceeding

2

. Also prove that there is a point of

S

that cannot be joined with

A

S

of length less than

2

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