From Newsgroup: rec.puzzles

Writing the in The Proceedings of London Mathematical society, Series II,
Vol. 14, Part 4, Mr. Eric H Neville writes the following:

"A familiar figure at fairs and shows is the sportsman with a cloth on
which a large circle is painted and five smaller equal circular discs of
thin metal, who offers the holiday-maker some considerable reward if he
can lay the five discs on the cloth in such a way that no part of the
large circle can be seen, the experimenter of course paying for each
attempt. At a time when work of a more serious kind was for a few days impossible to me, I welcomed the problem of calculating the best
arrangement of the discs, and the least value of the ratio of their radius
to that of the painted circle, and the results may interest others" ...

<https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms/
s2_14.1.308>

I've arrived at a ratio of what seems a reasonable approximation of the
ratio of the radius of the smaller circles to the radius of the larger
circle (0.6333...), by geometry and construction, but the resulting discs
do seem somewhat easy to place. Can anyone do better and get closer to the limit?

I understand that the article quoted provides an approximate range of the solution, to seven decimal places, but I don't have access to the full
article to see it. Dudeney mentions the puzzle and quotes Neville's answer
in the solution to puzzle 287 - The Circle and Discs.
--
David Entwistle
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From Newsgroup: rec.puzzles


David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> posted:

Writing the in The Proceedings of London Mathematical society, Series II, Vol. 14, Part 4, Mr. Eric H Neville writes the following:

"A familiar figure at fairs and shows is the sportsman with a cloth on
which a large circle is painted and five smaller equal circular discs of thin metal, who offers the holiday-maker some considerable reward if he
can lay the five discs on the cloth in such a way that no part of the
large circle can be seen, the experimenter of course paying for each attempt. At a time when work of a more serious kind was for a few days impossible to me, I welcomed the problem of calculating the best
arrangement of the discs, and the least value of the ratio of their radius to that of the painted circle, and the results may interest others" ...

<https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms/ s2_14.1.308>

I've arrived at a ratio of what seems a reasonable approximation of the ratio of the radius of the smaller circles to the radius of the larger circle (0.6333...), by geometry and construction, but the resulting discs
do seem somewhat easy to place. Can anyone do better and get closer to the limit?

I understand that the article quoted provides an approximate range of the solution, to seven decimal places, but I don't have access to the full article to see it. Dudeney mentions the puzzle and quotes Neville's answer in the solution to puzzle 287 - The Circle and Discs.

See https://bobson.ludost.net/copycrime/mgardner/gardner02.pdf (page 141)
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From Newsgroup: rec.puzzles

On Tue, 27 Jan 2026 22:44:57 GMT, Ilan Mayer wrote:

See https://bobson.ludost.net/copycrime/mgardner/gardner02.pdf (page
141)

Excellent, thanks. I had indeed been working towards figure 59, but was perplexed by the ease of placing disc five, in that arrangement. The explanation of the actual solution, as per figure 60, makes a lot more
sense.
--
David Entwistle
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