Problem K. 799. (February 2024)

K. 799. Misi lives in a street with detached houses only. If we count which house Misi lives in from the beginning of the street on his side, we get twice as many as if we counted which house Misi lives in from the end of the street on the same side. The houses are numbered consecutively from 1 starting at the beginning of the street, with odd numbers on the left and even numbers on the right. Misi's house is on the left side when looking at it from the beginning of the street. Had the houses been numbered from the end, the number of Misi's house would be 25 less than it is now. How many houses are there on that side of the street where Misi lives?

(5 pont)

Deadline expired on March 11, 2024.

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

Megoldás. Ha az utca elejétől indulva Misiék a \(\displaystyle 2x\)-edik házban laknak a bal (páratlan) oldalon, akkor házszámuk \(\displaystyle 2(2x)-1 = 4x-1\). Ha az utca végétől számoznák a házakat, akkor Misiék a páros oldalon laknának, és a házszámuk \(\displaystyle 2x\) lenne (mert innen indulva az \(\displaystyle x\)-edik házban laknának). A megadott összefüggés alapján \(\displaystyle 4x-1-25=2x\), innen \(\displaystyle x=13\). Tehát az utcában \(\displaystyle 13+26–1= 38\) ház van Misiék oldalán.

Statistics:

73 students sent a solution.
5 points:	Csabai Samu, Csáki Anikó, Farkas Simon, Fülöp Magdaléna, Gáti Benjamin, Hajnal Ákos Huba, Juhász Zsombor, Károly Kamilla , Kőhidi Kata, Máté Kristóf, Olajos Anna, Pázmándi Renáta , Piller Zsófia, Sajó Marcell 16, Sipos Dániel Sándor, Sipos Levente, Szabó Máté, Szalóki Árpád, Szedmák Szabrina, Tamás Attila Gábor, Válek Péter.
4 points:	Chen Peidong, Dóry Johanna, Feith Benedek, Juhász Gergely, Kóródy Vera, Németh Ábel, Ördög Dominik, Pintér Lilianna, Szőke János, Timár Vince , Tóth Bálint Levente, Viczián Adél.
3 points:	5 students.
1 point:	2 students.
0 point:	1 student.
Not shown because of missing birth date or parental permission:	32 solutions.

Problems in Mathematics of KöMaL, February 2024