"Ice-pick" was accepted as an alternative answer.
An interesting distinction. The weapon that was used to murder Leon Trotsky is nearly always described (in quizzes, at least) as an ice pick. But there's always some confusion: was it an ice pick, or an ice axe?
What's the difference, you may ask. Well, I'll tell you: an ice pick is something that you might use to break up ice cubes before you put them in your gin & tonic; an ice axe is something that you would use, if you were a mountaineer or a winter climber (which you may be, for all I know), to enable you to scale icy slopes - and to arrest your slide in the event of a fall.
That's my opinion, at least; for others, it's not so clear cut. Wikipedia, for example, on its Ice pick page, says "The term ice pick also commonly refers to a mountaineers' tool known in the USA as an ice axe."
On its Ice axe page, however, Wikipedia doesn't mention the mountaineers' tool being known as an ice pick. But it does say that the head of an ice axe features both a pick and an adze.
Oxford Dictionaries defines an ice axe as a tool used by mountaineers, but an ice pick as either "A small pick used by climbers to traverse ice-covered slopes" (my italics) or "A sharp, straight, pointed implement with a handle, used to break ice into small pieces for chilling food and drinks." It gives no fewer than 20 examples of the use of 'ice pick' in what it interprets as the former sense (a mountaineer's tool), but crucially (for me), only four of them - at the most - can have been written by mountaineers. Five of them mention Trotsky!
I myself have climbed mountains on five continents, and used ice axes on three. I also like to consider myself something of a minor authority on climbing literature. And I don't remember ever hearing a mountaineer (from the USA or elsewhere) referring to an ice axe as an ice pick.
In the 1992 film Basic Instinct, Sharon Stone murders her lover with what is invariably described as an icepick. In this case, it's clearly the implement used to separate ice cubes, and not the mountaineer's tool. One has to wonder whether the scriptwriter was inspired by the Trotsky murder; but Ms. Stone had no easy task in committing murder with this particular weapon; she had to tie her victim up first (with a silk scarf), and then sit on him, and it took several blows and involved a lot of blood. One imagines that the Trotsky murder was much quicker and simpler.
(If you've never seen Basic Instinct, don't worry: this is not a spoiler – it happens in the opening scene. And you may be surprised to hear that this is not the most memorable scene in the film. Although, if you are ... where have you been?!)
So now we come back to the original question: "What was used to assassinate Leon Trotsky?"
The delightfully-named Murderpedia has two photographs of the actual weapon (photos 18 and 19, near the bottom of the page). And by my definition, it's unquestionably an ice axe. USA Today has one of the same pictures (in a report about the weapon resurfacing, 60-odd years after being stolen from police premises) – and it consistently calls it an icepick. The article doesn't include the word 'axe' (or even 'ax') anywhere.
So the bottom line is that the MQL question setter was clearly quite right to allow both answers ("ice axe" and "ice pick"). Especially, IMHO, as he or she gave "axe" first and allowed "pick" as an alternative answer.
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