Henry Ernest Dudeney/Modern Puzzles/129 - The Circle and Discs

Modern Puzzles by Henry Ernest Dudeney: $129$

During a recent visit to a fair we saw a man with a table,

on the oilcloth covering of which was painted a large red circle,

and he invited the public to cover this circle entirely with five tin discs which he provided,

and offered a substantial prize to anyone who was successful.

The circular discs were all of the same size, and each, of course, smaller than the red circle.

he showed that it was "quite easy when you know how," by covering up the circle himself without any apparent difficulty,

but many tried over and over again and failed every time.

It was a condition that when once you had placed any disc you were not allowed to shift it,

otherwise, by sliding them about after they had been placed, it might be tolerably easy to do.

Let us assume that the red circle is six units in diameter.

Now, what is the smallest possible diameter for the five discs in order to make a solution possible?

1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $129$. -- The Circle and Discs
1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Circle Puzzles: $287$. The Circle and Discs