Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 464. (September 2015)

K. 464. A teacher instructed the students to count from 1 to 1000 while keeping the following rules. In each calculation step, one can choose to either multiply the previous result by a fixed one digit number \(\displaystyle a\) selected in advance, or just add 1 to it. Which number should be chosen to be \(\displaystyle a\) in order to be able to reach 1000 in the least number of steps?

(6 pont)

Deadline expired on October 12, 2015.


152 students sent a solution.
6 points:Barabás Bence, Debreczeni Tibor, Dobák Dániel, Hoffmann Balázs, Mészáros 916 Márton, Pálvölgyi Szilveszter, Póta Balázs, Szűcs Leó, Vas Miklós.
5 points:Barta Ákos, Dékány Barnabás, Farkas Norbert, Kertész Ferenc, Koleszár Panna, Mónos Péter, Németh 728 Ágnes Sára, Piller Ádám.
4 points:22 students.
3 points:57 students.
2 points:11 students.
1 point:11 students.
0 point:25 students.
Unfair, not evaluated:9 solutions.

Problems in Mathematics of KöMaL, September 2015