Mathematical and Physical Journal
for High Schools
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Problem B. 3922. (September 2006)

B. 3922. I have a six-digit number in mind. By transferring the first digit to the end, I would obtain three times the original number. What is my number?

(3 pont)

Deadline expired on October 16, 2006.


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

Megoldás: Legyen a gondolt szám N=\overline{abcdef}, ekkor az új szám

3N=\overline{bcdefa}=10N-999999a,

ahonnan N=999999a/7=142857a. Nyilván a\le3, hiszen 3a\leb\le9. Ha a=3 lenne, akkor b=9 lehetne csak, de akkor 3N már hétjegyű szám lenne. Ezért a feladatnak legfeljebb két megoldása lehet: N1=142857 és N2=285714, melyek közül mindkettő eleget tesz a feltételnek.


Statistics:

496 students sent a solution.
3 points:410 students.
2 points:51 students.
1 point:19 students.
0 point:15 students.
Unfair, not evaluated:1 solution.

Problems in Mathematics of KöMaL, September 2006