Suppose someone kills more people than they intended. Did they murder the extra people?

As noted in other answers, if you intend to murder the expected occupants of the arena, then you have murdered the others. However there are interesting exceptions...

For one exception, if the intended 60,000 victims in the arena had been legally sentenced to death, and the bomb is the chosen method of execution, then you have not murdered them. Execution is lawful killing and is not murder. And for another exception, if the victims are all members of the armed forces whose country is at war with yours, then again killing soldiers in a war is not murder, even if they happen to kicking back at a festival. In an exception to the exception though, if the execution victims were having a last visit from their families when the bomb was set off, or the soldiers had their families with them, then the 60,000 family members would have been murdered but the intended victims would not have been.

You might also not be guilty of murder if you didn't know you were planting a bomb (maybe you thought you were just leaving a backpack for a friend who works there), or if you didn't know that the button you were pressing would set off a bomb. There are various interesting novels (Charles Stross's Rule 34 springs to mind) about conspiracies recruiting "useful idiots" where each one carries out part of the overall plan, and each individual step does not appear controversial but the end result is fatal.

If you can think of a scenario where planting a bomb would be lawful self-defence then that too could stop this being murder, although honestly I'm not sure how you'd justify that!

Yes, you are responsible for the knock-on effects of your criminal actions, but there’s a line.

For instance suppose you aimed to commit tax fraud by understating your company’s profits in the accounting system. Your limited partner sees those fake numbers, believes they are real, believes this means essential cancer treatments are unaffordable, and commits suicide rather than face a painful and slow death. Did you commit murder? No, courts will generally say not, because the causality chain is simply too weak, too improbable, too Rube Goldberg. Murder is not a foreseeable knock-on effect of tax fraud.

However, if you’re robbing a party store, and shoot a display merely to scare the clerk, and unbeknownst a child was hiding behind the display, that’s murder because it was the product of a serious crime.

The reasoning is that anytime there’s an armed robbery, while murder is not the objective, a killing is a foreseeable risk; and an armed robber reasonably ought to know that and thus is responsible when mayhem does occur. After all, the armed robber had the option to eliminate that risk by not doing an armed robbery.

There’s a parallel concept in civil law, called “Eggshell Skull”: where if your action against someone is a tort, but has knock-on effects you couldn’t possibly imagine... you are still liable for them. There was a famous case where a child kicked another child in class; routine stuff. But

It turned out that the victim had an unknown microbial condition that was irritated, and resulted in him entirely losing the use of his leg. No one could have predicted the level of injury. Nevertheless, the court found that the kicking was unlawful because it violated the "order and decorum of the classroom", and the perpetrator was therefore fully liable for the injury.

Yeah. Don’t kick people in class.

This could fall under the Felony Murder Rule which is a specific type of "transfer of intent" where if someone dies while you are committing (or even aiding in!) a felony you can be guilty of first-degree murder. Some restrictions apply, which depend on jurisdiction, but generally "terrorism" is going to get you every time in the US, and setting a bomb at a crowded music festival would fall under the modern definition of terrorism.

So first-degree murder would apply to anyone who died as a result of this, regardless of how many people you actually intended to harm. In many local jurisdictions it's even looser, even if you didn't intend to harm anyone but only wanted to do extensive property damage, even if your bomb didn't hurt anyone directly but gave someone a heart attack, etc.

Don't kill people. Don't commit felonies. Definitely don't do the two of them at the same time.

To add a perspective from a different legal system:

In Germany, this would fall under the notion of Eventualvorsatz (loosely translated, "recklessness"). Basically, whenever the criminal code requires intent ("Vorsatz" in German), a total lack of consideration for the consequences of an action can be counted as being equivalent to intent. In other words, if I did not specifically intend X, but totally ignore the fact that X is a likely consequence of what I do, that counts as an intentional act. The concept is similar to that of "depraved-heart murder" in US law_{Thanks to Tiercelet for mentioning this.}.

A typical example would be setting fire to an inhabited house - while you may not intend to kill the inhabitants, it is still highly likely that they will be killed, so a court might consider this to be (attempted) murder, even absent any explicit intention to kill. For example, in 2015, a firefighter in was found guilty of intended murder for setting fire to the building he lived in, because there were other inhabitants - even though his main intention was suicide.

This would probably cover your case - deliberately setting off a bomb in a crowded place is certainly likely to kill, even if that was not your specific goal.

Murder is defined as the unlawful intentional killing of a person, and not the intentional performance of an act which results in an unlawful death. Therefore, if you intend to kill 200,000 people but kill only 1 person, that is 1 count of murder, and if you intend to kill 1 person but do kill 200,000, that is 200,000 counts of murder. You don't even need to intend to kill anyone – you could just intend to main 1 person. The scope of "intend" is with respect to the act, and not the result. If you only intend to rescue some number of people and harm none but do kill someone, you do not have the intent to act unlawfully so it's not murder. However, it could well be some other variety of homicide, since even accidentally killing a person through criminal negligence is a kind of homicide.