Mathematical and Physical Journal
for High Schools
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Problem A. 728. (September 2018)

A. 728. Floyd the flea makes jumps on the positive integers. On the first day he can jump to any positive integer. From then on, every day he jumps to another number that is not more than twice his previous day's place.

a) Show that Floyd can make infinitely many jumps in such a way that he never arrives at any number with the same sum of decimal digits as at a previous place.

b) Can the flea jump this way if we consider the sum of binary digits instead of decimal digits?

Dürer competition, 2015

(7 pont)

Deadline expired on October 10, 2018.


28 students sent a solution.
7 points:Matolcsi Dávid, Schrettner Jakab, Szabó Kristóf, Weisz Máté.
6 points:Szabó 417 Dávid.
4 points:1 student.
3 points:7 students.
2 points:8 students.
1 point:3 students.
0 point:3 students.
Not shown because of missing birth date or parental permission:1 solutions.

Problems in Mathematics of KöMaL, September 2018