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.

### Statistics:

 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