Comments on: Domino Functions https://programmerluddite.com/2013/04/domino-functions/ The Blog of Barney Boisvert, Software Craftsman Wed, 08 Jan 2014 06:07:03 +0000 hourly 1 http://wordpress.org/?v=3.9.1 By: Bill Beers https://programmerluddite.com/2013/04/domino-functions/#comment-2579 Wed, 26 Jun 2013 05:04:40 +0000 http://programmerluddite.com/?p=69#comment-2579 As I read this post, I had a flashback to one of my college math courses(Number Theory), where my professor told us of a German math prodigy named, Carl Friedrich Gauss.

There is a well known story about Karl Friedrich Gauss when he was in
elementary school. His teacher got mad at the class and told them to
add the numbers 1 to 100 and give him the answer by the end of the
class. About 30 seconds later Gauss gave him the answer.

Looking at your triangle it clicked.
1 + 2 + 3 + … + n

If you take the sequence and add it to the reverse sequence, shown below… 

1      2    3    4    5    6    7    8    9   10   11   12
+    +    +    +    +    +    +    +   +     +    +     +
12   11  10   9    8    7    6    5    4     3     2     1
=
13   13   13   13   13   13   13   13   13   13   13 =  12(13) = 156 or n(n+1)

which is double the total, so take 1/2 of that to find the total = 78
78 != 91 so this made me go, hmmm
But, since the dominos are 0 based, it really is 1+…+13 so plug in 13 for n

13(14)
--------      =  182/2 = 91
2

Math is cool.

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