Question 20
a) Nico chooses 10 distinct positive integers, then Uriel chooses 6 and adds them. Uriel wins if the sum is a multiple of 6 and loses otherwise. Can Nico choose the 10 numbers so that Uriel cannot win?
b) Nico chooses 11 distinct positive integers, then Uriel chooses 6 and adds them. Uriel wins if the sum is a multiple of 6 and loses otherwise. Can Nico choose the 11 numbers so that Uriel cannot win?
In each case, give an example if yes and explain why if no.
b) Nico chooses 11 distinct positive integers, then Uriel chooses 6 and adds them. Uriel wins if the sum is a multiple of 6 and loses otherwise. Can Nico choose the 11 numbers so that Uriel cannot win?
In each case, give an example if yes and explain why if no.