Difference between revisions of "1981 IMO Problems/Problem 6"
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== Solution 2 == | == Solution 2 == | ||
− | We can start by creating a list consisting of certain x an y values and their outputs. <cmath>f(0,0)=1 f(0,1)=2 f(0,2)</cmath> | + | We can start by creating a list consisting of certain x an y values and their outputs. <cmath>f(0,0)=1, f(0,1)=2, f(0,2)=3, f(0,3)=4,</cmath> |
Revision as of 20:55, 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 |
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Solution 2
We can start by creating a list consisting of certain x an y values and their outputs.