Difference between revisions of "1997 PMWC Problems/Problem I8"

Latest revision as of 12:16, 15 January 2008

$997-996-995+994+993-992+991-990-989+988+989-986+\cdots+7-6-5+4+3-2+1=?$

Wee look for a pattern:

+--++-+--++-+

So the pattern is +--++-. We find the value of one round:

$(n-(n-1)-(n-2)+(n-3)+(n-4)-(n-5))=1$

So we just need to find the number of rounds.

There are 6 terms per round, and the +1 doesn't belong to a round, so 996/6=166

$1(166)+1=167$

@@ Line 4: / Line 4: @@
 ==Solution==
-{{solution}}
+Wee look for a pattern:
++--++-+--++-+
+So the pattern is +--++-. We find the value of one round:
+<math>(n-(n-1)-(n-2)+(n-3)+(n-4)-(n-5))=1</math>
+So we just need to find the number of rounds.
+There are 6 terms per round, and the +1 doesn't belong to a round, so 996/6=166
+<math>1(166)+1=167</math>
+==See Also==
+{{PMWC box|year=1997|num-b=I7|num-a=I9}}
+[[Category:Introductory Algebra Problems]]