Re: 61. - THE SILVER CUBES

On Sat, 12 Jul 2025 23:14:47 -0000 (UTC), Richard Tobin wrote:

The first solution can be found in seconds with a fairly straighforward
program.  Obviously Dudeney didn't do that.

No, in the introduction to the same book the author discusses the non-
trivial factors of the sequence of (base 10) numbers comprised just of
one's: 1, 11, 111, 1111....

He explains that the number comprising seventeen ones has two factors and
lists them, but explains that no one knows if the number comprising
nineteen ones has a non-trivial divisor...

The later footnote included with the solution for a related problem says:

"Mr Oscar Hoppe, of New York, informs me that, after reading my statement
in the Introduction, he was led to investigate the case of n = 19, and
after long and tedious work he succeeded in proving the number to be
prime. He submitted his proof to the London Mathematical Society, and a
specially appointed committee of that body accepted the proof as final and
conclusive. He refers me to the Proceedings of the Society for 14th
February 1918".

Well done Mr Oscar Hoppe.

--
David Entwistle