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?

See The Solution Submitted by Federico Kereki

Rating: 4.1667 (6 votes)

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Puzzle Solution

Comment 4 of 4 |

Using three THREES

---------------------------------

N = limit d/dx (x*x*.......*x)

x-> 3^(3-3)

Using two TWOS

---------------------------

N = limit d/dx (x*x*........*x)

x-> 2/2

Without using any NUMBERS

-----------------------------------------------

N = d/dx (x+x+.......+x)

--------------------

N x's

Edited on August 28, 2022, 10:37 pm

Posted by K Sengupta on 2022-08-28 22:36:31

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