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 solutionss.

Problems in Mathematics of KöMaL, November 2010

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 solutionss.

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