• The object of the game is to bring PEACE to the world for Thanksgiving using linear algebra. HOWEVER YOU MUST WORK ALONE ON THIS PROBLEM.
• Work in the field of F of integers modulo seven and set child=PEACE=0, dragon=NATIONALISM=1, wizard=DEMAGOGUERY=2, sorceress=FAMINE=3, unicorn=IDEALISM=4, hydra=WAR=5, lephrechaun=GREED=6.
• Observe the results of pressing the buttons. They act independently. Think about it for a while....
• Find a system of equations over F whose solution will tell you how to win the game.
• Solve the system of equations using linear algebra. Be careful, the only numbers allowed in F are 0-6. You cannot multiply by one-half. Before you start, you might want to figure out the multiplicative inverses of 2,3,4,5,6 in F. For example 3 times 5 is 15 which is 1 modulo 7 so 3 and 5 are multiplicative inverses.
• How many solutions are there to the game? What is the minimum number of buttons that must be pushed to win the game?
• Write up and explain your solution.
• Thanks to Diego Ongaro for writing most of the code!