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50 - or more (Posted on 2020-09-10) Difficulty: 4 of 5
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.

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.

No Solution Yet Submitted by Ady TZIDON    
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Hints/Tips some hints & remarks @ Ch | Comment 3 of 14 |
Ch, the triplet chosen by you is definitely better than mine - i tried 9,9,9  and your 4,9,9 can be easily transformed into mine since !4=9.

However  I have squeezed out of nine significantly more single digits:
  sqrt9=3  3!=6 6!=720 !3=2 !2=1
   plus !4=9   and !(4+1)=44 and 4!!=8    ETC

Just by adding those transformations we can fill in some holes in your list   35 =36-1; 37=36+1; 41=44-3; 44=!(4+1): 47=44+3:   53=44+9;.....59 not solved yet, 62=64-2; 65=64+1;   89=81+8=9*9+4!!
Did not extend your list,  but still leave it to you,
 if 92 or 93 can be represented  as the rules permit ----we have an improved answer.


  Posted by Ady TZIDON on 2020-09-10 17:12:53
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