Problem K/C. 783. (October 2023)
K/C. 783. Pilots refer to directions by using the face of a clock. For example, they say 12 o'clock instead of north, 3 o'clock instead of east. Follow the flight of a reconnaissance aeroplane that started from the army base on the ground, flew 1 minute in the direction of 1 o'clock, 2 minutes in the direction of 2 o'clock, 3 minutes in the direction of 3 o'clock, 10 minutes in the direction of 4 o'clock, 5 minutes in the direction of 5 o'clock, 6 minutes in the direction of 6 o'clock, 7 minutes in the direction of 7 o'clock, 8 minutes in the direction of 8 o'clock, 9 minutes in the direction of 9 o'clock, 4 minutes in the direction of 10 o'clock, 11 minutes in the direction of 11 o'clock, and 12 minutes in the direction of 12 o'clock. The speed of the plane relative to the ground remained the same throughout. What path would have been the shortest from the starting point to the final destination?
(5 pont)
Deadline expired on November 10, 2023.
Sorry, the solution is available only in Hungarian. Google translation
Megoldás. Minden iránynak van egy ellentéte: 1 órának 7 óra, 2-nek 8, 3-nak 9, 4-nek 10, 5-nek 11 és 6-nak 12. Ha az ellentétes irányba repüléseket összegezzük, akkor 4 óra, 7 óra, 8 óra, 9 óra, 11 óra és 12 óra irányba kell \(\displaystyle 6-6\) percet repülnünk. A 4 óra irányába és a 8 óra irányába 6 perc repülés helyettesíthető 6 óra irányába történő 6 perc repüléssel, ami a 12 óra irányába való 6 perc repüléssel ,,ki is esik". A 7 óra irányú és 11 óra irányú \(\displaystyle 6-6\) perces repülés 9 óra irányú 6 perces repülésnek felel meg, amihez még ugyanennyi jön, azaz összesen 12 percnyit repült a gép 9 óra felé, azaz nyugatnak.
Statistics:
192 students sent a solution. 5 points: 71 students. 4 points: 14 students. 3 points: 4 students. 2 points: 7 students. 1 point: 12 students. 0 point: 33 students. Unfair, not evaluated: 4 solutionss. Not shown because of missing birth date or parental permission: 43 solutions.
Problems in Mathematics of KöMaL, October 2023