9 billion names of God the integer: Difference between revisions

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This task is a variation of the short story by Arthur C. Clark. Solvers should be aware of the consequences of completing this task, see: [http://en.wikipedia.org/wiki/The_Nine_Billion_Names_of_God#Plot_summary Plot summary of The Nine Billion Names of God].
This task is a variation of the short story by Arthur C. Clark. Solvers should be aware of the consequences of completing this task, see:
* [[wp:The Nine Billion Names of God#Plot_summary|Plot summary of The Nine Billion Names of God]].

In detail, to specify what is meant by a “name”
:The integer 1 has 1 name 1.
:The integer 2 has 2 names 1+1, and 2.
:The integer 1 has 1 name “1”.
:The integer 3 has 3 names 1+1+1, 2+1, and 3.
:The integer 2 has 2 names “1+1”, and 2.
:The integer 4 has 5 names 1+1+1+1, 2+1+1, 2+2, 3+1, 4.
:The integer 3 has 3 names “1+1+1”, “2+1”, and “3”.
:The integer 5 has 7 names 1+1+1+1+1, 2+1+1+1, 2+2+1, 3+1+1, 3+2, 4+1, 5.
:The integer 4 has 5 names “1+1+1+1”, “2+1+1”, “2+2”, “3+1”, “4”.
:The integer 5 has 7 names “1+1+1+1+1”, “2+1+1+1”, “2+2+1”, “3+1+1”, “3+2”, “4+1”, “5”.


;Task
The task is to display the first 25 rows of a number triangle which begins:
The task is to display the first 25 rows of a number triangle which begins:
<pre>
<pre>
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</pre>
</pre>


Where row n corresponds to integer n, and each column C in row n from left to right corresponds to the number of names begining with C.
Where row <math>n</math> corresponds to integer <math>n</math>, and each column <math>C</math> in row <math>m</math> from left to right corresponds to the number of names begining with <math>C</math>.


A function G(n) should return the sum of the names for that row. Demonstrate this function by displaying: G(23), G(123), G(1234), and G(12345).
A function <math>G(n)</math> should return the sum of the names for that row. Demonstrate this function by displaying: <math>G(23)</math>, <math>G(123)</math>, <math>G(1234)</math>, and <math>G(12345)</math>.


Extra credit.
;Extra credit


If your environment is able, plot G(n) against n for n=1 to n=999.
If your environment is able, plot <math>G(n)</math> against <math>n</math> for <math>n=1\ldots 999</math>.

Revision as of 14:08, 27 April 2013

Task
9 billion names of God the integer
You are encouraged to solve this task according to the task description, using any language you may know.

This task is a variation of the short story by Arthur C. Clark. Solvers should be aware of the consequences of completing this task, see:

In detail, to specify what is meant by a “name”

The integer 1 has 1 name “1”.
The integer 2 has 2 names “1+1”, and 2.
The integer 3 has 3 names “1+1+1”, “2+1”, and “3”.
The integer 4 has 5 names “1+1+1+1”, “2+1+1”, “2+2”, “3+1”, “4”.
The integer 5 has 7 names “1+1+1+1+1”, “2+1+1+1”, “2+2+1”, “3+1+1”, “3+2”, “4+1”, “5”.
Task

The task is to display the first 25 rows of a number triangle which begins: 

                                      1
                                    1   1
                                  1   1   1 
                                1   2   1   1
                              1   2   2   1   1
                            1   3   3   2   1   1

Where row corresponds to integer , and each column in row from left to right corresponds to the number of names begining with .

A function should return the sum of the names for that row. Demonstrate this function by displaying: , , , and .

Extra credit

If your environment is able, plot against for .

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