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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.)
Some thoughts | Comment 1 of 14
1 +
2 +=
3 ++=
4 +=
5 ++++=
6 +===+=
7 ++++++=
8 +=
9 ++=
10 +=+===+=+=
11 ++++++++++=
12 +===+=

Every prime p is represented by p-1 '+'s followed by an '='. Similarily every power of a prime p^n is represented by p-1 '+'s followed by an '='.

6 and 12 also have the same pattern, so I suspect the pattern is based on the prime factors of the number .

I will conjecture:
13 ++++++++++++=
14 ?
15 ?
16 +=
17 ++++++++++++++++=
18 +===+= [same as 6, 12]
19 ++++++++++++++++++=
20 +=+===+=+= [same as 10]
  Posted by Brian Smith on 2004-02-20 14:31:35
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