Difference between revisions of "1997 PMWC Problems/Problem I8"
(New page: ==Problem== <math>997-996-995+994+993-992+991-990-989+988+989-986+\cdots+7-6-5+4+3-2+1=?</math> ==Solution== {{solution}}) |
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==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}} |
Revision as of 08:21, 9 October 2007
Problem
Solution
Wee look for a pattern:
+--++-+--++-+
So the pattern is +--++-. We find the value of one round:
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
See Also
1997 PMWC (Problems) | ||
Preceded by Problem I7 |
Followed by Problem I9 | |
I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 |