From Newsgroup: rec.puzzles

Does this work as a puzzle - I don't have an answer as yet?

Three spheres are resting in a (badly drawn) cone. Each sphere touches the side of the cone and any adjacent sphere.

https://ibb.co/PvMgh78H

If each sphere as an integer radius, what is the smallest radius of the
larger sphere?
--
David Entwistle
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From Newsgroup: rec.puzzles

On Fri, 5 Jun 2026 09:16:07 -0000 (UTC), David Entwistle wrote:

Each sphere touches the side of the cone and any adjacent sphere.

I perhaps should make this clearer - each sphere touches the side of the
cone, around the whole of the cone, and any adjacent sphere.
--
David Entwistle
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From Newsgroup: rec.puzzles


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

Does this work as a puzzle - I don't have an answer as yet?

Three spheres are resting in a (badly drawn) cone. Each sphere touches the side of the cone and any adjacent sphere.

https://ibb.co/PvMgh78H

If each sphere as an integer radius, what is the smallest radius of the larger sphere?

Some comments, probably erroneous, in rot13:

(1) Vfa'g guvf gur fnzr nf gur ceboyrz jvgu fcurer naq pbar ercynprq
jvgu pvepyr naq gevnatyr?
(2) Gurer ner guva pbarf naq guvpx pbarf, jvgu gur engvb orgjrra gur
fcurer'f enqvhf naq gur qvfgnapr sebz fcurer pragre gb gur pbar'f
iregrk orvat gur cnenzrgre (fvar).
Sbe nal pbar guvf cnenzrgre -- pnyy vg 1/C -- vf gur fnzr sbe rnpu fcurer.
(2n) (V jbeel gung vafgrnq Qnivq vagraqrq n svkrq cnenzrgre, r.t. fvar
bs sbegl-svir qrterff.)
(3) V frg gur fznyyrfg enqvhf gb 1. (Jvfushy guvaxvat?)
Fvzcyr nytroen yrnqf gb (C+1)/(C-1) sbe gur frpbaq enqvhf; yrg'f
gel C=3 gb trg n enqvhf bs gjb. Gur guveq enqvhf vf sbhe. Bar, gjb, sbhe.
(4) (Bar, k, k fdhnerq nyfb jbexf, ohg gur chmmyr nfxf sbe gur zvavzhz.)

------
Cheers,
James
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From Newsgroup: rec.puzzles

In article <10vu44n$10m78$2@dont-email.me>,
David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> wrote:

Does this work as a puzzle - I don't have an answer as yet?

Three spheres are resting in a (badly drawn) cone. Each sphere touches the >side of the cone and any adjacent sphere.

https://ibb.co/PvMgh78H

If each sphere as an integer radius, what is the smallest radius of the >larger sphere?

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By similar triangles, the radii of the successive spheres are in equal
ratios - they form a geometric progession.

The smallest sequence of three unequal integers in geometric
progression is 1, 2, 4.

-- Richard
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