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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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re(3): Record Comment 14 of 14 |
(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 fact--three "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 2020-09-17 07:11:11
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