SOLUTION: If you are given the sum of the squares of three consecutive integers, what four digits can never occur in the ones place? There are lots of things going on in this problem. I d

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Question 1043867: If you are given the sum of the squares of three consecutive integers, what four digits can never occur in the ones place?
There are lots of things going on in this problem. I don't want to give you any hints. What I want to see is people throwing out ideas on where to start, what to do first, what to do next, etc.
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
If you are given the sum of the squares of three consecutive integers, what four digits can never occur in the ones place?
There are lots of things going on in this problem. I don't want to give you any hints.
What I want to see is people throwing out ideas on where to start, what to do first, what to do next, etc.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

last     1       2        3                           last digit
digit n  n^2   (n+1)^2   (n+2)^2       sum 1+2+3      of the sum
1	 1	 4	 9		14		4	
2 	 4	 9	 6		19		9	
3	 9	 6	 5		20		0	
4	 6	 5	 6		17		7	
5	 5	 6	 9		20		0	
6	 6	 9	 4		19		9	
7	 9	 4	 1		14		4	
8	 4	 1	 0		5		5	
9	 1	 0	 1		2		2	
0	 0	 1	 4		5		5	
								Never occur: 1, 3, 6, 8


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