An unusual problem by Reddit user cgibbard, from a discussion in 2010:
Here’s a representation of 101010 for you to figure out.
* * *
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* * * * * * * * *
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* * * * * *
As a bonus, here’s the corresponding representation for 42:
* * *
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* * *
The puzzle is to find the rule for this representation.
A commenter wrote, “This puzzle is really clever and very rewarding to figure out.”
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SelectClick for Answer |
This thread contains two explanations:
By user typographicalerror:
Every prime is a tree. Every number is a forest whose trees correspond to the primes its prime factorization. The tree for 2 is a single vertex. The tree for any other prime is a root vertex connected to the forest representing your prime’s place in the list of all primes. (e.g., 7 is the 4th prime, so you create a root vertex and connect it to the representation for 4.)
By user root45:
Each prime number has it’s own tree and we simply put these trees together to represent multiplication. So, once we know what the trees look like for 3 and 7 we can put them next to each other to make 21.
To find out what the tree looks like for a prime, we build it recursively using the number of primes less than or equal to our prime. To start off with, 2 is just a dot (*).
2: *
To make the tree for 3 we note that there are 2 primes less than or equal to 3, so we take the tree for 2 and connect it to another * like so:
3:
*
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*
To make 4 we first prime factor 4 as 2*2 and then put the trees next to each other.
4: * *
To make 7 we note that there are 4 primes less than or equal to 7, so we take the forest for 4 and connect it to a root.
7:
* *
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*
Now we can make the tree for 21 = 3*7.
21:
* * *
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* *
So basically you can recursively define each number using prime factorization and the number of primes less than or equal to a prime. Note that the function that gives this number is called π(x) (that is, ‘pi of x’).
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