Game theory: Finding the core

Question

$v(1234) = 4$

$v(123) = v(124) = v(134) = v(234) = 3$

$v(12) = 2$

$v(13) = v(14) = v(23) = v(24) = v(34) = 1$

$v(1) = v(2) = v(3) = v(4) = 0$

What is the core of this game?

Answer 1

Hint: Suppose that core includes an allocation where one of the players gets more than $1$. What would happen in light of the payoffs $v(123) = v(124) = v(134) = v(234) = 3$?