Three coins are tossed, and $X$ is the number of tails minus the number of heads. What values can $X$ take?

Explanation

1. 01

   With $t$ tails there are $3 - t$ heads, so $X = t - (3 - t) = 2t - 3$.

2. 02

   For $t = 0, 1, 2, 3$: $X = -3, -1, 1, 3$.