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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.

So:
1=1
6=1+5
9=5*2-1
13=15-2
27=51-4!
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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Some Thoughts another, higher | Comment 2 of 14 |
Using 4, 9 and 9: 

   RPN               Algebraic

 1  9,9/          9/9
 2  4v            sqrt(4)
 3  9v            sqrt(9)
 4  49v,9+v       sqrt((sqrt(49)+9))
 5  9,4-          9-4
 6  9v!           (sqrt(9))!
 7  49v           sqrt(49)
 8  4,9v^v        sqrt(4^sqrt(9))
 9  9,9*v         sqrt((9*9))
10  4,9v!+        4+(sqrt(9))!
11  4v,9+         sqrt(4)+9
12  4,9v*         4*sqrt(9)
13  4,9+          4+9
14  9,4-,9+       9-4+9
15  4!,9-         (4)!-9
16  49v,9+        sqrt(49)+9
17  4,9v^v,9+     sqrt(4^sqrt(9))+9
18  9,9+          9+9
19  4,9+,9v!+     4+9+(sqrt(9))!
20  4v,9+,9+      sqrt(4)+9+9
21  49,9*v        sqrt((49*9))
22  4,9+,9+       4+9+9
23  4!,9,9/-      (4)!-9/9
24  4!            (4)!
25  4!,9,9/+      (4)!+9/9
26  4!,9v!,9v/+   (4)!+(sqrt(9))!/sqrt(9)
27  9,9v*         9*sqrt(9)
28  4,9v^,9v!!+v  sqrt((4^sqrt(9)+((sqrt(9))!)!))
29  4v,9,9v*+     sqrt(4)+9*sqrt(9)
30  4!,9v!+       (4)!+(sqrt(9))!
31  4,9,9v*+      4+9*sqrt(9)
32  9v!,9v!*,4-   (sqrt(9))!*(sqrt(9))!-4
33  4!,9+         (4)!+9
34  9v!,9v!*,4v-  (sqrt(9))!*(sqrt(9))!-sqrt(4)
35  
36  4,9*          4*9
37  
38  4v,9v!,9v!*+  sqrt(4)+(sqrt(9))!*(sqrt(9))!
39  4,9+,9v*      (4+9)*sqrt(9)
40  49,9-         49-9
41  
42  49v,9v!*      sqrt(49)*(sqrt(9))!
43  49,9v!-       49-(sqrt(9))!
44  
45  4,9*,9+       4*9+9
46  49,9v-        49-sqrt(9)
47  
48  4,9,9v+*      4*(9+sqrt(9))
49  49            49
50  9,9v!*,4-     9*(sqrt(9))!-4
51  4!,9,9v*+     (4)!+9*sqrt(9)
52  49,9v+        49+sqrt(9)
53  
54  9,9v!*        9*(sqrt(9))!
55  49,9v!+       49+(sqrt(9))!
56  4v,9,9v!*+    sqrt(4)+9*(sqrt(9))!
57  9,9*,4!-      9*9-(4)!
58  49,9+         49+9
59  
60  4,9,9v!+*     4*(9+(sqrt(9))!)
61  4,9v^,9v-     4^sqrt(9)-sqrt(9)
62  
63  49v,9*        sqrt(49)*9
64  4,9v^         4^sqrt(9)
65  
66  4v,9+,9v!*    (sqrt(4)+9)*(sqrt(9))!
67  4,9v^,9v+     4^sqrt(9)+sqrt(9)
68  
69  4!,9v*,9v-    (4)!*sqrt(9)-sqrt(9)
70  4,9v^,9v!+    4^sqrt(9)+(sqrt(9))!
71  
72  4!,9v*        (4)!*sqrt(9)
73  4,9v^,9+      4^sqrt(9)+9
74  
75  99,4!-        99-(4)!
76  9v!!,9/,4-    ((sqrt(9))!)!/9-4
77  9,9*,4-       9*9-4
78  4,9+,9v!*     (4+9)*(sqrt(9))!
79  9,9*,4v-      9*9-sqrt(4)
80  9v!!,9/       ((sqrt(9))!)!/9
81  9,9*          9*9
82  4v,9v!!,9/+   sqrt(4)+((sqrt(9))!)!/9
83  4v,9,9*+      sqrt(4)+9*9
84  9,4^v,9v+     sqrt(9^4)+sqrt(9)
85  94,9-         94-9
86  
87  9,4^v,9v!+    sqrt(9^4)+(sqrt(9))!
88  94,9v!-       94-(sqrt(9))!
89  
90  9,4^v,9+      sqrt(9^4)+9
91  94,9v-        94-sqrt(9)
92  
93  

  Posted by Charlie on 2020-09-10 15:17:37
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