In this answer, I do not prove that eating a pack of cigarettes is safe. (Please don't do it!)
However, I show that there is a common belief that a pack of cigarettes would contain enough nicotine to kill an adult is based on a urban legend. (That doesn't mean it is wrong, just that it hasn't been proven right.)
This is based on this article:
The author explains there is a commonly quoted toxic level:
Standard textbooks, databases, and safety sheets consistently state that the lethal dose for adults is 60 mg or less (30–60 mg), leading to safety warnings that ingestion of five cigarettes or 10 ml of a dilute nicotine-containing solution could kill an adult.
[Special Note: There are two claims here. One is about the lethality of 60mg of nicotine, which is challenged below. The other is that five cigarettes contains (only) 60mg of nicotine. I do not challenge this in this answer. @DavePhD has since added an answer that provides a good reference to refute this claim, which casts my conclusion in doubt. Please give consideration to his answer.]
However, the scientific literature doesn't support that 60mg is lethal. Instead:
The literature reports on fatal nicotine intoxications suggest that the lower limit of lethal nicotine blood concentrations is about 2 mg/L, corresponding to 4 mg/L plasma, a concentration that is around 20-fold higher than that caused by intake of 60 mg nicotine. Thus, a careful estimate suggests that the lower limit causing fatal outcomes is 0.5–1 g of ingested nicotine, corresponding to an oral LD50 of 6.5–13 mg/kg. This dose agrees well with nicotine toxicity in dogs, which exhibit responses to nicotine similar to humans
(Reminder: Not everyone responds the same way to a poison. "LD50" is a dose that is toxic enough to be a lethal dose to 50% of the population.)
If these figures are correct, eating a pack of cigarettes is not enough to kill 50% of the people who try it.
However, you might be someone who reacts more strongly than the median person or there may be other toxic ingredients that are in cigarettes that haven't been considered here, so this should not be read as a go ahead to eat cigarettes.