5
Part of 2012 May Olympiad
Problems(2)
27 boxes, each has >=12 marbles May Olympiad (Olimpiada de Mayo) 2012 L1 P4
Source:
9/29/2021
There are boxes located in a row; each contains at least marbles. The allowed operation is transfer a ball from a box to its neighbor on the right, as long as said neighbor contains more pellets than the box from which the transfer will be made. We will say that a distribution initial of the balls is happy if it is possible to achieve, by means of a succession of permitted operations, that all the balls are in the same box. Determine what is the smallest total number of marbles with the that you can have a happy initial layout.
combinatorics
Number of friends
Source: Olimpiada de Mayo 2012 (first level) #5
6/5/2012
There are 12 people such that for every person A and person B there exists a person C that is a friend to both of them. Determine the minimum number of pairs of friends and construct a graph where the edges represent friendships.
floor functioncombinatorics proposedcombinatorics