Difference between revisions of "1993 IMO Problems/Problem 6"
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Latest revision as of 11:31, 21 November 2023
Problem
There are 
lamps 
in a circle (
), where we denote 
. (A lamp at all times is either on or off.) Perform steps 
as follows: at step 
, if 
is lit, switch 
from on to off or vice versa, otherwise do nothing. Initially all lamps are on. Show that:
(a) There is a positive integer 
such that after steps all the lamps are on again;
(b) If 
, we can take 
;
(c) If 
, we can take 
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 1993 IMO (Problems) • Resources | ||
| Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Last Problem |
| All IMO Problems and Solutions | ||
