Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 145. (December 2007)

K. 145. Charlie is planning to go on a trip around the world with his land rover. He is going to cover 42\;000 km on land. A tyre lasts 24\;000 km on any of the car's wheels. How many tyres does he need to buy, and how should they be placed on the wheels so that they last for the whole journey?

(6 pont)

Deadline expired on January 10, 2008.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. A négy keréknek összesen 168000 km-t kell mennie, ez pontosan hét gumi teljes menettávolsága. Hét gumi elegendő is, ehhez 6000 km-enként ciklikusan kell cserélni őket. Az alábbi négyesek lesznek fenn egyszerre, a gumikat 1-7-ig számozva: 1234, 2345, 3456, 4567, 5671, 6712, 7123. Minden gumi pontosan 4 csoportban van benne, tehát mindegyik 24000 km-t fog menni.


185 students sent a solution.
6 points:107 students.
4 points:20 students.
3 points:5 students.
2 points:11 students.
1 point:1 student.
0 point:30 students.
Unfair, not evaluated:11 solutions.

Problems in Mathematics of KöMaL, December 2007