Difference between revisions of "1981 IMO Problems/Problem 6"
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== Solution 2 == | == Solution 2 == | ||
+ | \begin{center} | ||
+ | \begin{tabular}{ c c c } | ||
+ | cell1 & cell2 & cell3 \\ | ||
+ | cell4 & cell5 & cell6 \\ | ||
+ | cell7 & cell8 & cell9 | ||
+ | \end{tabular} | ||
+ | \end{center} |
Revision as of 21:48, 8 April 2024
Problem
The function satisfies
(1)
(2)
(3)
for all non-negative integers . Determine
.
Solution
We observe that and that
, so by induction,
. Similarly,
and
, yielding
.
We continue with ;
;
; and
;
.
It follows that when there are 1984 2s, Q.E.D.
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
1981 IMO (Problems) • Resources | ||
Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Last question |
All IMO Problems and Solutions |
https://beastacademy.com/ https://beastacademy.com/
Solution 2
\begin{center} \begin{tabular}{ c c c }
cell1 & cell2 & cell3 \\ cell4 & cell5 & cell6 \\ cell7 & cell8 & cell9
\end{tabular} \end{center}