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Repeated addition (Posted on 2004-02-20) Difficulty: 4 of 5
+
+=
++=
+=
++++=
+===+=
++++++=
+=
++=
+=+===+=+=
++++++++++=
+===+=

Explain the pattern and find the next five rows.

Hint: the symbols I chose have nothing to do with the pattern.

See The Solution Submitted by Tristan    
Rating: 4.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Yes! Comment 14 of 14 |

Here is how to get the nth row:

For the numbers 1 to n, put a + for a number that is relatively prime to n and a = for a number that has a common factor with n. The nth row is the pattern of symbols that repeats.

1. +

2. +=

3. ++=

4. +=

5. ++++=

6. +===+=

7. ++++++=

8. +=

9. ++=

10. +=+===+=+=

11. ++++++++++=

12. +===+=

Next 5 rows:

13. ++++++++++++=

14. +=+=+===+=+=+=

15. ++=+==++==+=++=

16. +=

17. ++++++++++++++++=

 


  Posted by Math Man on 2011-01-19 18:13:36
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