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

 

 

Order KöMaL!

Competitions Portal

C. 867. Starting from the origin in the usual Cartesian coordinate system, a broken line segment is drawn. We arrive back at the y-axis in every fourth step, see the figure.

Using a certain ball-pen and a coordinate system with unit length of 0.5 cm, we draw broken line segments of length 8000 meters as in the figure. Count how many times we arrive back at the y-axis.

(5 points)

Deadline expired on 15 November 2006.


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

Megoldás.

[(1+3+\ldots+(2n-1))\sqrt2+(5+11+\ldots+(6n-1))]\cdot\frac{1}{2}\leq800\,000,

n^2\sqrt2+3n^2+2n\leq1600\,000,

(3+\sqrt2)n^2+2n\leq1\,600\,000.

Másodfokú egyenlőtlenség megoldása nélkül is kitalálható, hogy melyik a legnagyobb n egész szám, amire teljesül: n=601.


Statistics on problem C. 867.
459 students sent a solution.
5 points:235 students.
4 points:21 students.
3 points:19 students.
2 points:27 students.
1 point:72 students.
0 point:66 students.
Unfair, not evaluated:19 solutions.


  • Problems in Mathematics of KöMaL, October 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