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hectoc is a puzzle, where one is given a sequence of six decimal digits and the task is to intersperse arithmetic operations from the given set $+,-,/,*$ and matching brackets $(,)$ in a way that the resulting valid arithmetic expression yields $100$.

The example on the homepage illustrates the task: $123456\mapsto 1+(2+3+4)*(5+6)=100$


Questions:

  • have hectoc-type diophantine equations already been recognized by the professional mathematics community and if yes,

    • what is their formal generalized definition; (apparently one needs at least a finite sequence of digits, a set of symbols denoting operations or precedence and a set of rules for valid expressions)?
    • which theoretical results are available regarding proving/disproving existence of solutions and methods for finding solutions?

  • which possible applications for hectoc-type equations can be envisaged?

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  • $\begingroup$ What literature searches have you tried? Gerhard "Perhaps It's Found Under Dudeney" Paseman, 2018.05.21. $\endgroup$
    – Gerhard Paseman
    Commented May 21, 2018 at 15:20
  • $\begingroup$ @GerhardPaseman I have done some online search for the term "hectoc", but didn't get anything beyond the official site and a link to a German TV show, where a 12 year old kid challenged an adult on playing hectoc and won (I saw that show and it was the first time I heard of hectoc). How is Dudeney related to hectoc? Is he the same Dudeney who coined the term "trisectors" for people who believe to have a solution for provably unsolvable problems? $\endgroup$
    – Manfred Weis
    Commented May 21, 2018 at 15:42
  • $\begingroup$ I don't know about trisectors. H. E. Dudeney was a puzzlist whose recreational mathematics included graph theory, geometric dissections, alphanumeric problems, and likely progenitors of hectoc. If there has been any good endorsement or research of hectoc done at all (most likely through recreational mathematics or some part of computer science), I would expect it to have a reference to Dudeney. Gerhard "You Could Ask Will Shortz" Paseman, 2018.05.21. $\endgroup$
    – Gerhard Paseman
    Commented May 21, 2018 at 15:50
  • $\begingroup$ Regarding trisectors: I confused Underwood Dudley with Dudeney: The Trisectors $\endgroup$
    – Manfred Weis
    Commented May 21, 2018 at 16:22
  • $\begingroup$ To save others the effort, I note there are no results for hectoc on MathSciNet. $\endgroup$
    – Gerry Myerson
    Commented May 22, 2018 at 1:52

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