perplexus.info :: Just Math : Three threes, or two twos?

Three threes, or two twos? (Posted on 2003-12-09)

You can represent ANY positive integer n using only three twos by writing

n= -log₂(log₂(√√...√2))

where log₂ is the logarithm base 2, and there are n square roots.

Can you manage to do the same (that is, represent all positive integers) using three THREEs instead? And by using only TWO twos?

Submitted by Federico Kereki

Rating: 4.1667 (6 votes)

Solution: (Hide)

The solution is radically different:
N=lim_x-->3^(3-3) ^d/_dx (x*x*..*x)
where '^' and '*' stand for exponentiation and multiplication, and there are N x's in the product. Using x--> 2/2 gives the other solution.
Of course, you can also do without NO numbers at all, and just write
N=^d/_dx (x+x+...+x)
with N x's in the sum...

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Solution	K Sengupta	2022-08-28 22:36:31
Nice Puzzle	K Sengupta	2007-03-16 10:52:33
Look Ma, no numbers!	e.g.	2003-12-12 12:52:01
f(x) = x+1	Brian Smith	2003-12-09 15:43:35

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info