All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
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    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
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.

6!!!=18     







  Posted by Ady TZIDON on 2020-09-10 17:12:53
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (3)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information