Let's start with a triplet of integers, say (1, 2, 5) and a set of mathematical operations (+, , *, /, ^, sqrt, fact!, concatenation, brackets).
Our task will be to represent all (or almost all  as explained below) integers from 1 to n using some or all of the initial triplet and any quantity of operations defined above.
So:
1=1
6=1+5
9=5*21
13=152
27=514!
60=12*5 etc
Let's define n as the first occurrence of not being able to find a valid representation for n+1 and for n+2. I believe that in our case n=17 (15+2), since neither 18 nor 19 get valid solutions.
You are requested to find a triplet of integers (a,b,c) enabling a maximal n.
(In reply to
re(2): Record by Dej Mar)
Indeed, all the "outside the box" thinking that's possible seems to make moot the request for a maximal value.
While the letter of the puzzle stated "integers", the spirit (given in the example) three examples in factthree "integers", were all single digits. The only concatenation in the examples was of pure unmodified digits. No subfactiorials or multifactorials were in the examples, and no use of square brackets to indicate floor.

Posted by Charlie
on 20200917 07:11:11 