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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)

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Solution no algorithm | Comment 12 of 14 |

Basically the + means same and = means different. First I noticed that there are at most as many characters as the number of the row. Then I noticed that all the primes followed the same pattern. (x-1) +'s and one =. From there I assumed that all the rows started out like that but then were changed depending on it's factors.

1)  +
2)  +=
3)  ++=
4)  +=
5)  ++++=
6)  +===+=
7)  ++++++=
8)  +=
9)  ++=
10) +=+===+=+=
11) ++++++++++=
12) +===+=

13 is easy...
13) ++++++++++++=

with 14, I took the 2 factors of it and copied one over the other, then repeated the pattern until there were 14 characters. and where ever the columns matched 14 would get a +. If they were different it got a =

2)   +=+=+=+=+=+=+=
7)   ++++++=++++++=
14) +=+=+===+=+=+=

continuing, the other lines are...

15) ++=+==++==+=++=
16) +=
17) ++++++++++++++++=

and lastly, if it resulted in a repeating pattern (with square numbers or numbers that had factors that were square) then the pattern was just reduced. and for that one persont that wonder what 30 would be I got this using 2 3 5 6 10 15...

30) +=====+===+=+===+=+===+=====+=

...the one thing I don't get is why 1 doesn't fit the pattern. According to "(x-1) +'s and a ="  1 should just be a =.


  Posted by Danny on 2004-05-16 17:13:20
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