Guest Posted March 26, 2008 Report Share Posted March 26, 2008 11 cups are on a table, all of them are upside down. You must turn all of them right side up, inverting 3 at a time. How many moves will it take? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 26, 2008 Report Share Posted March 26, 2008 5 turns (assuming you MUST turn 3 over each time) DDDDDDDDDDD 11 down UUUDDDDDDDD-1 3 up 8 down UUDUUDDDDDD-2 4 up 7 down (turned one of the up back to down and 2 to up) UUDUDUUDDDD-3 5 up 6 down (again turned one of the up back to down) UUDUDUUUUUD-4 8 up 3 down UUUUUUUUUUU-5 11 up Obviously, there can be different orders here as well. Quote Link to comment Share on other sites More sharing options...
0 EventHorizon Posted March 26, 2008 Report Share Posted March 26, 2008 (edited) 5 turns (assuming you MUST turn 3 over each time) DDDDDDDDDDD 11 down UUUDDDDDDDD-1 3 up 8 down UUDUUDDDDDD-2 4 up 7 down (turned one of the up back to down and 2 to up) UUDUDUUDDDD-3 5 up 6 down (again turned one of the up back to down) UUDUDUUUUUD-4 8 up 3 down UUUUUUUUUUU-5 11 up Obviously, there can be different orders here as well. Yup statman is right. With 3 moves, you can flip at most 9 cups With 4 moves, you can flip all the cups, but would have needed to flip one back over. With 5 moves, there will be 15 total flips...which is 11 plus an even number...so you can flip two cups 3 times and the rest once. 2 cups flipped 3 times + 9 cups flipped 1 time = 6+9 = 15 total cup flips 15 / 3 = 5 moves So it will take at least 5 moves of inverting 3 at a time....but it is possible to do it with any odd number of moves greater than or equal to 5. Edited March 26, 2008 by EventHorizon Quote Link to comment Share on other sites More sharing options...
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11 cups are on a table, all of them are upside down. You must turn all of them right side up, inverting 3 at a time. How many moves will it take?
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