Difference between revisions of "2015 OIM Problems/Problem 6"
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== Problem == | == Problem == | ||
| − | Beto plays the following game with his computer: initially his computer randomly chooses 30 numbers from 1 to 2015, and Beto writes them on a blackboard (there may be numbers repeated); At each step, | + | Beto plays the following game with his computer: initially his computer randomly chooses 30 numbers from 1 to 2015, and Beto writes them on a blackboard (there may be numbers repeated); At each step, Beto chooses a positive integer <math>k</math> and some of the numbers written in the blackboard, and subtracts the number <math>k</math> from each of them, with the condition that the numbers resulting results remain non-negative. The objective of the game is to achieve that at some point all 30 resulting numbers equal 0, in which case the game ends. Find the smallest number <math>n</math> such that, regardless of the numbers he initially chose the computer from him, Beto can finish the game in at most <math>n</math> steps. |
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
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== See also == | == See also == | ||
| + | [[OIM Problems and Solutions]] | ||
Latest revision as of 14:06, 14 December 2023
Problem
Beto plays the following game with his computer: initially his computer randomly chooses 30 numbers from 1 to 2015, and Beto writes them on a blackboard (there may be numbers repeated); At each step, Beto chooses a positive integer 
and some of the numbers written in the blackboard, and subtracts the number from each of them, with the condition that the numbers resulting results remain non-negative. The objective of the game is to achieve that at some point all 30 resulting numbers equal 0, in which case the game ends. Find the smallest number 
such that, regardless of the numbers he initially chose the computer from him, Beto can finish the game in at most steps.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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