Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem C. 900. (May 2007)

C. 900. 75% of a certain three-digit number of different digits consists of the same digits as the original number but with no digit in the same place. Which number is it?

(5 pont)

Deadline expired on June 15, 2007.


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

Megoldás. Lehet 3.abc=4.bca vagy 3.abc=4.cab. Vagyis 296a=370b+37c vagy 397c=260b+26c. Az első esetben 8a=10b+c. A második eset nem jöhet létre, mert 397c csak úgy lehetne 13-mal osztható, ha c is osztható 13-mal.

Az a lehetséges 10 értékét végignézve nyolc háromjegyű megoldást kapunk: 216, 324, 432, 540, 648, 756, 864, 972.


Statistics:

172 students sent a solution.
5 points:120 students.
4 points:21 students.
3 points:4 students.
2 points:7 students.
1 point:3 students.
Unfair, not evaluated:17 solutions.

Problems in Mathematics of KöMaL, May 2007