[ July 5, 2026 ] [ Last update [ -- ]
Smallest and largest products of three threedigital
substrings of a ninedigital.
A puzzle from Simplementenumeros.blogspot.com

At a first unconsidered moment one might think that from the lowest ninedigital
\(123*456*789\mathbf{\color{blue}{\;=\;}}44253432\)
is the smallest solution and that from the highest ninedigital
\(987*654*321\mathbf{\color{blue}{\;=\;}}207204858\)
is the largest solution.
Nothing could be further from the truth because here are the correct solutions:

\(\bbox[#DEFDD1,8px,border:1px yellow solid]{{\Large147*258*369\mathbf{\color{blue}{\;=\;}}13994694}}\)
and
\(\bbox[#DEFDD1,8px,border:1px yellow solid]{{\Large941*852*763\mathbf{\color{blue}{\;=\;}}611721516}}\)

There is a pattern emerging as the lowest product is made from the column digits
that you find back on your average numerical keyboard from bottom to top.