Mathematical and Physical Journal
for High Schools
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Problem B. 4734. (October 2015)

B. 4734. Some fields (unit cubes) constituting a cubical lattice of edge 2015 units are infected by an unknown disease. The disease will spread if at least \(\displaystyle t\) fields in some row parallel to any edge of the cube are infected \(\displaystyle (1 \le t \le 2015)\). In that case, every field of that row will become infected in one minute. Én is javaslok egyet: How many fields need to be infected initially in order to

\(\displaystyle a)\) make it possible

\(\displaystyle b)\) be certain

that the infection reaches all fields of the cube?

Proposed by G. Mészáros, Budapest

(6 pont)

Deadline expired on November 10, 2015.


Statistics:

61 students sent a solution.
4 points:12 students.
3 points:10 students.
2 points:14 students.
1 point:15 students.
0 point:8 students.
Unfair, not evaluated:2 solutions.

Problems in Mathematics of KöMaL, October 2015