KöMaL - Mathematical and Physical Journal for Secondary Schools
Hungarian version Information Contest Journal Articles News
Entry form to the contest
Problems and solutions
Results of the competition
Problems of the previous years



Order KöMaL!

Competitions Portal

C. 838. Mihály Tímár (the hero of a famous Hungarian novel) is in a trouble. The red crescent that marked the sack containing the treasure has come off. He knows, however, that the heaviest of the four sacks hides the treasure. From three measurements, he has found out that the first sack together with the second one are lighter than the other two, the first and third together are equal in weight to the other two, and the first and fourth sacks together are heavier than the other two. Which sack hides the treasure?

(5 points)

Deadline expired on 15 February 2006.

Google Translation (Sorry, the solution is published in Hungarian only.)

Megoldás: A zsákok tömege legyen: a, b, c, d. Ekkor: a+b<c+d, a+c=b+d, a+d>b+c. Két-két összefüggés összegéből kapjuk:

2a+b+c<c+b+2d, vagyis a<d.

a+b+2c<a+b+2d, vagyis c<d.

a+2b+c<a+c+2d, vagyis b<d.

Így a negyedik zsákban van a kincs.

Statistics on problem C. 838.
447 students sent a solution.
5 points:369 students.
4 points:7 students.
3 points:14 students.
2 points:21 students.
1 point:10 students.
0 point:25 students.
Unfair, not evaluated:1 solution.

  • Problems in Mathematics of KöMaL, January 2006

  • Our web pages are supported by:   Ericsson   Google   Cognex   Emberi ErőforrĂĄs TĂĄmogatĂĄskezelő   Emberi ErőforrĂĄsok MinisztĂŠriuma  
    OktatĂĄskutatĂł ĂŠs Fejlesztő IntĂŠzet   Nemzeti TehetsĂŠg Program     Nemzeti
KulturĂĄlis Alap   ELTE   Morgan Stanley