2018 November Team #8
Source:
November 13, 2018
geometry3D geometry
Problem Statement
Tessa has a unit cube, on which each vertex is labeled by a distinct integer between 1 and 8 inclusive. She also has a deck of 8 cards, 4 of which are black and 4 of which are white. At each step she draws a card from the deck, and[*]if the card is black, she simultaneously replaces the number on each vertex by the sum of the three numbers on vertices that are distance 1 away from the vertex;[*]if the card is white, she simultaneously replaces the number on each vertex by the sum of the three numbers on vertices that are distance away from the vertex.When Tessa finishes drawing all cards of the deck, what is the maximum possible value of a number that is on the cube?