Mathematical and Physical Journal
for High Schools
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Problem K. 267. (November 2010)

K. 267. Given that \overline{ab} +\overline{acb} =2\cdot \overline{ba}, where \overline{ab} and \overline{ba} are two-digit numbers and \overline{acb} is a three-digit number, determine the values of the digits in the addition if c=0.

(6 pont)

Deadline expired on December 10, 2010.


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

Megoldás. Az \(\displaystyle a\) és \(\displaystyle b\) számjegyekkel a feladat feltétele \(\displaystyle (10a+b)+(100a+10\cdot 0+b)=2(10b+a)\), azaz \(\displaystyle 110a+2b=20b+2a\). Innen \(\displaystyle 6a=b\), amiből \(\displaystyle a\) és \(\displaystyle b\) számjegyek lévén az \(\displaystyle a=b=0\) illetve \(\displaystyle a=1\), \(\displaystyle b=6\) következik. A feladat határozottan két- és háromjegyű számokról szól, ezért az első megoldást elvetjük. A keresett számjegyek az \(\displaystyle a=1\) és \(\displaystyle b=6\).


Statistics:

240 students sent a solution.
6 points:82 students.
5 points:44 students.
4 points:73 students.
3 points:22 students.
2 points:3 students.
1 point:7 students.
0 point:1 student.
Unfair, not evaluated:8 solutions.

Problems in Mathematics of KöMaL, November 2010