Difference between revisions of "2017 IMO Problems/Problem 5"
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An integer <math>N \ge 2</math> is given. A collection of <math>N(N + 1)</math> soccer players, no two of whom are of the same height, stand in a row. Sir Alex wants to remove <math>N(N - 1)</math> players from this row leaving a new row of <math>2N</math> players in which the following <math>N</math> conditions hold: | An integer <math>N \ge 2</math> is given. A collection of <math>N(N + 1)</math> soccer players, no two of whom are of the same height, stand in a row. Sir Alex wants to remove <math>N(N - 1)</math> players from this row leaving a new row of <math>2N</math> players in which the following <math>N</math> conditions hold: | ||
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Show that this is always possible. | Show that this is always possible. | ||
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| + | ==Solution== | ||
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| + | ==See Also== | ||
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| + | {{IMO box|year=2017|num-b=4|num-a=6}} | ||
Latest revision as of 01:42, 19 November 2023
Problem
An integer 
is given. A collection of 
soccer players, no two of whom are of the same height, stand in a row. Sir Alex wants to remove 
players from this row leaving a new row of 
players in which the following 
conditions hold:
(
) no one stands between the two tallest players,
(
) no one stands between the third and fourth tallest players,
() no one stands between the two shortest players.
Show that this is always possible.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 2017 IMO (Problems) • Resources | ||
| Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 6 |
| All IMO Problems and Solutions | ||
