coverOn Friday I posted this puzzle….

Three men decide to have a shooting contest to the death. Each man has one gun, and each gun contains just one bullet.  They draw straws to determine the order in which they will shoot. The rules are simple:
If the first man to fire shoots the second man, then the third man has to shoot the first man. If the first man to fire shoots the third man, then second man has to shoot the first man.  Oh, and the first person has to shoot.
What should first man do to ensure that he survives the contest?
If you have not tried to solve it, have a go now.  For everyone else the answer is after the break.

The first man should shoot into the air.  The second man will shoot the third man because he is the only one who still has a bullet.

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle(UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.


    1. The one who shoots second will be the second one there the third one can’t shoot anymore.
      Also the contest still goes on because it was to the death. So, after the second man shoots the third man, the first and the second men will race for the gun of the third man with the last bullet still not fired.

  1. What? The answer makes no sense. What happened to the third mans bullet? In any case the remaining people only have to shoot if the first one shoots someone. If he does not then the arrangement is null and void. What a waste of time.

    1. The third man’s bullet remains unused as he’d find it hard to shoot it after he’s dead 😉
      It was a confusingly worded puzzle, granted, but it does make sense.

    1. I agree. My answer was indeed that the first man should miss both targets, but my assumption was that everyone would live, because the rules didn’t state what would happen if nobody was hit.

  2. I think that’s a poor answer.
    Mine was that the first man shot the second man in a vulnerable but soft part of his body at point blank, the bullet continuing on to kill the third man.

  3. He could go into a position where the second and third man are lined up, one behind the other. Then he will shoot the second man in the neck, and the bullet will enter and exit the second man, and kill the third also. I know this is highly unlikely to happen, but still it’s a possibility.

  4. Yes, what sirkitkat said. I think the first man should shoot Richard for presenting such an idiotic “puzzle”.

  5. I thought of that answer, but I thought it would not ensure survival. That’s because the two living man would soon run to the dead man, grab the gun and try to shoot each other.

    1. Man 2 and man 3 can’t shoot each other with one gun which has one bullet. Unless they line themselves up so that the single bullet goes through both of them.

  6. The answer should be:
    The first man deliberately shoots his bullet in the air, thus it was not intended for either the second or third man. This forces the second and third men to fire at each other, since the first man is no longer a threat having run out of ammo and both the second and third men still have a bullet each. Hopefully killing each other in the process.

    1. The second and third men can’t shoot each other as they have to shoot in the order that was determined by the drawing of the straws. Man 2 shoots man 3. Man 3 is dead.

    1. Well, this is not OK. The puzzle states “… to ensure …”. This means whatever happens after his action, he will survive.
      The problem now is: what if the second man also shoots in the air? In this case the third man has the possibility to select who to kill. Because of this the “.. to ensure..” part of the puzzle is not fulfilled.

    2. @Anne Elk, In case you are the second person and you know that the third person is very angry on the first person, you may just shoot in the air to ensure that the last person is going to kill the first one…

  7. I’d only like to point to a spelling error in the original post: the word ‘puzzle’ in this case is missing a ‘z’.

  8. I don’t see how this answer can be deduced from what’s given in the puzzle. If it was stated that everyone has to shoot, in the order determined by the drawing of straws, and that each aims to preserve his own life, then it seems logical that the second person will shoot the third. (This assumes, I suppose, that one person trying to shoot another will result in a successful kill, or else the third person will still get a shot.) But the puzzle doesn’t rule out the possibility that, say, if person one shoots in the air then person two will shoot him.

    1. First of all it’s not a deduction but more of a solution. There may be other solutions. Secondly, if person 2 shoots person 1 then person 3 will shoot either person 2. This puzzle assumes that each person is acting rationally within the rules. Your possibility is irrational as if person two shoots person one then person 3 will shoot person two. I’m assuming when you say “him” you mean person one.

  9. The first person robs the gun from one of the other persons. Because they are not allowed to shoot back and the promise of a quick death (instead of long a painful death) the first person will gain access of two or three guns …

  10. It took me a while to work out who was ‘the first man’. Was it first man as in merely a label such as person A or did it mean first person to shoot. If the later it meant there was no the first person could shot either of the other men and live. But why that should mean if he shot in the air one of the others wouldn’t shot him immediately took a little while to work out.

    1. The ‘names’ of the men are determined by the order they shoot in and the order they shoot in is determined by the drawing of the straws. Man one is called man one because he has drawn the straw that determines that he shoots first and the second and third men the same.

  11. I thought it was a Russian roulette scenario – they have one bullet each but they don’t know which chamber it’s in. Which makes the answer much more complicated

  12. And I think both B and C would forget their differences and shoot A for being a smartarse. Clearly they can’t stand the guy anyway

  13. If the first man shoots in the air he has shot neither second nor third man so the rules have fallen apart, the contest is null and void and it’s time to light up.

    1. The rules that you have misread have not fallen apart. It merely states that they shoot. It doesn’t say at what. Shoot in this instance does not necessarily mean to shoot at someone. It means to fire the gun.

  14. I also considered this solution, but it does not satisfy the condition of “ensure”. Firing into the air leaves uncertainty as to the other shooters’ actions.

    Better solution: Shooter 1 pistol whips 2, then shoots 3. 1 picks up both remaining guns, shoots 2 and saves the last bullet for the person that set up this sick game.

    1. You must remember that the puzzle is assuming rationality. If not then there are more possibilities. Rationality is not stated but I suppose it should have been.

      If everyone acts (within this puzzle where there is no world outside of this puzzle) RATIONALLY then there is no uncertainty. If man one shoots in the air, man two must shoot man three because if he doesn’t then man three will shoot him (man two).

  15. I considered this as a solution, but it does not satisfy the condition of “ensure”. After firing into the air, the shooter cannot be certain what will happen.

    Better solution: 1 pistol whips 2, then shoots 3. He then gathers the remaining guns, shoots 2, and saves the last bullet for the person that wrote this puzzle.

  16. Shooter 1 shoots number 2. Number 3 can’t fire waiting for his turn, he waits for number 2 to shoot, but number 2 is dead… solved it!!!

    1. The rules say that if number 2 dies, number 1 will be killed by number 3. So that isn’t a solution.

    2. It also says “They draw straws to determine the order in which they will shoot” So these rules contradict.

  17. My solution is that the first man says to the others – “Give me your gun and I will shoot the other one.”

  18. Puzzle is not well-stated, thus the confusion. This is how it could’ve been better stated: (1) three people, each with a gun and a bullet; (2) each can only shoot his gun in a specified order (A, B, C); (3) if A shoots B, then C shoots A; (4) if A shoots C, then B shoots A; (5) A must shoot his gun; (6) (most importantly) each person will act to maximize his chances of staying alive (note: “maximize his chances of” not “guarantee”). What should A do?

  19. I thought “first”, “second” and “third” referred to this: “They draw straws to determine the order in which they will shoot”, i.e. if the first man shoots the second man, the third man waits indefinitely for the second man to shoot.

  20. Richard’s answer is correct but his following state is not. “The second man will shoot the third man because he is the only one who still has a bullet.”. Both the second man and third man have a bullet in their guns. If “The second man will shoot the third man” then it is only the third man (now dead or dying) who still has a bullet in his gun. I suppose the first man and the second man might rush for the third man’s gun to use it to shoot the other. Now if this later part is allowed then it does not guarantee survival of the first man as the second man might get the third man’s gun and shoot the first man.

    1. The sentence you quote is ambiguous, but the ‘he’ must refer to the third man, i.e. the second man will shoot the third man (rather than the first) because only the third poses a threat.

  21. The trouble is, the rules don’t state the second and third men can’t shoot the first man anyway, whether he fires his gun into the air or not. So I think the first man could be in trouble whatever he does…

    1. No, no and thrice no. The puzzle assumes that all are acting rationally with the bounds of the puzzle. It is irrational for man 2 to shoot man 1 because man 3 will shoot man 2. If man 2 shoots man 3 then there is no one left to shoot and therefore both man 1 and man 2 survive. If you don’t assume rationality (as many seem to be doing) then almost anything goes which means there’s no point in giving the puzzle in the first place.

  22. That was the answer I came to in a couple of seconds, but forgot that the second man had to do something.

    Is that an analogy for Scotland’s Housed Nuclear ‘Detterent’?

  23. The whole setup doesn’t make sense. ‘Three men decide to have a shooting contest to the death’ – why ‘decide’ to have a contest to the death and then void the whole thing by shooting in the air? If they were forced into the contest I could understand the solution….

  24. This was one of my solutions, but it requires a lot of assumptions, and I don’t think it “ensures” his survival. You’d need a few more rules to ensure anything.

    1. Gus
      On Friday you said that you had four solutions.
      Could you let us know what all four are please?

    2. I think this is really more of a thought experiment that a puzzle so we shouldn’t get bogged down too much about the ‘rules’ that don’t appear to be stated. It’s not meant to be water tight, just a very interesting thought experiment.

    3. The ‘whole thing’ is not voided because man 1 shoots in the air. The act of man 1 shooting in the air forces the puzzle in to the solution that man 2 must shoot man 3, assuming that all are acting rationally with the bounds of the world of this puzzle.

  25. I arrived at the suggested answer very quickly = IF > THEN > ELSE logic.

    However, having read so many comments rubbishing that answer because of how the question was posed, I have to agree with the dissenters.

    “Three men decide to have a shooting contest to the death”.

    How many suicidal/murderous psychopaths will give up after shooter 1 deliberately misses the others, just because “them’s the rules”?

    1. I don’t see it as a puzzle needing solid rules with no ‘loopholes’ but more of a thought experiment. The lack of solidity makes it more interesting than if it simply had one answer.

    2. The ancient Greek deiknymi, or thought experiment, “was the most ancient pattern of mathematical proof”, and existed before Euclidean mathematics,[2] where the emphasis was on the conceptual, rather than on the experimental part of a thought-experiment. Perhaps the key experiment in the history of modern science is Galileo’s demonstration that falling objects must fall at the same rate regardless of their masses. This is widely thought [3] to have been a straightforward physical demonstration, involving climbing up the Leaning Tower of Pisa and dropping two heavy weights off it, whereas in fact, it was a logical demonstration, using the ‘thought experiment’ technique. The ‘experiment’ is described by Galileo in Discorsi e dimostrazioni matematiche (1638) (literally, ‘Mathematical Discourses and Demonstrations’) thus:
      Salviati. If then we take two bodies whose natural speeds are different, it is clear that on uniting the two, the more rapid one will be partly retarded by the slower, and the slower will be somewhat hastened by the swifter. Do you not agree with me in this opinion?
      Simplicio. You are unquestionably right.
      Salviati. But if this is true, and if a large stone moves with a speed of, say, eight while a smaller moves with a speed of four, then when they are united, the system will move with a speed less than eight; but the two stones when tied together make a stone larger than that which before moved with a speed of eight. Hence the heavier body moves with less speed than the lighter; an effect which is contrary to your supposition. Thus you see how, from your assumption that the heavier body moves more rapidly than ‘ the lighter one, I infer that the heavier body moves more slowly.[4]
      Although the extract does not convey the elegance and power of the ‘demonstration’ terribly well, it is clear that it is a ‘thought’ experiment, rather than a practical one. Strange then, as Cohen says, that philosophers and scientists alike refuse to acknowledge either Galileo in particular, or the thought experiment technique in general for its pivotal role in both science and philosophy. (The exception proves the rule — the iconoclastic philosopher of science, Paul Feyerabend, has also observed this methodological prejudice.[5])
      Instead, many philosophers prefer to consider ‘Thought Experiments’ to be merely the use of a hypothetical scenario to help understand the way things actually are.
      Variety [edit]

      There are many different kinds of thought experiments. All thought experiments, however, employ a methodology that is a priori, rather than a posteriori, in that they do not proceed by observation or physical experiment.
      Thought experiments have been used in a variety of fields, including philosophy, law, physics, and mathematics. In philosophy, they have been used at least since classical antiquity, some pre-dating Socrates. In law, they were well-known to Roman lawyers quoted in the Digest.[6] In physics and other sciences, notable thought experiments date from the 19th and especially the 20th century, but examples can be found at least as early as Galileo.
      Origins and use of the literal term [edit]

      Johann Witt-Hansen established that Hans Christian Ørsted was the first to use the Latin-German mixed term Gedankenexperiment (lit. thought experiment) circa 1812.[7] Ørsted was also the first to use its entirely German equivalent, Gedankenversuch, in 1820.
      Much later, Ernst Mach used the term Gedankenexperiment in a different way, to denote exclusively the imaginary conduct of a real experiment that would be subsequently performed as a real physical experiment by his students.[8] Physical and mental experimentation could then be contrasted: Mach asked his students to provide him with explanations whenever the results from their subsequent, real, physical experiment differed from those of their prior, imaginary experiment.
      The English term thought experiment was coined (as a calque) from Mach’s Gedankenexperiment, and it first appeared in the 1897 English translation of one of Mach’s papers.[9] Prior to its emergence, the activity of posing hypothetical questions that employed subjunctive reasoning had existed for a very long time (for both scientists and philosophers). However, people had no way of categorizing it or speaking about it. This helps to explain the extremely wide and diverse range of the application of the term “thought experiment” once it had been introduced into English.
      Uses [edit]

      In its broadest usage, thought experimentation is the process of employing imaginary situations to help us understand the way things really are (or, in the case of Herman Kahn’s “scenarios”, understand something about something in the future). The understanding comes through reflection upon this imaginary situation. Thought experimentation is a priori, rather than an empirical process, in that the experiments are conducted within the imagination (i.e., Brown’s (1993) “laboratory of the mind”), and never in fact.
      Thought experiments, which are well-structured, well-defined hypothetical questions that employ subjunctive reasoning (irrealis moods) – “What might happen (or, what might have happened) if . . . ” – have been used to pose questions in philosophy at least since Greek antiquity, some pre-dating Socrates (see Rescher 1991). In physics and other sciences many famous thought experiments date from the 19th and especially the 20th Century, but examples can be found at least as early as Galileo.
      Thought experiments have been used in philosophy, physics, and other fields (such as cognitive psychology, history, political science, economics, social psychology, law, organizational studies, marketing, and epidemiology). In law, the synonym “hypothetical” is frequently used for such experiments.
      Regardless of their intended goal, all thought experiments display a patterned way of thinking that is designed to allow us to explain, predict and control events in a better and more productive way.
      Theoretical consequences [edit]
      In terms of their theoretical consequences, thought experiments generally:
      challenge (or even refute) a prevailing theory, often involving the device known as reductio ad absurdum, (as in Galileo’s original argument, a proof by contradiction),
      confirm a prevailing theory,
      establish a new theory, or
      simultaneously refute a prevailing theory and establish a new theory through a process of mutual exclusion.
      Practical applications [edit]
      Thought experiments can produce some very important and different outlooks on previously unknown or unaccepted theories. However, they may make those theories themselves irrelevant, and could possibly create new problems that are just as difficult, or possibly more difficult to resolve.
      In terms of their practical application, thought experiments are generally created in order to:
      challenge the prevailing status quo (which includes activities such as correcting misinformation (or misapprehension), identify flaws in the argument(s) presented, to preserve (for the long-term) objectively established fact, and to refute specific assertions that some particular thing is permissible, forbidden, known, believed, possible, or necessary);
      extrapolate beyond (or interpolate within) the boundaries of already established fact;
      predict and forecast the (otherwise) indefinite and unknowable future;
      explain the past;
      the retrodiction, postdiction and hindcasting of the (otherwise) indefinite and unknowable past;
      facilitate decision making, choice and strategy selection;
      solve problems, and generate ideas;
      move current (often insoluble) problems into another, more helpful and more productive problem space (e.g., see functional fixedness);
      attribute causation, preventability, blame and responsibility for specific outcomes;
      assess culpability and compensatory damages in social and legal contexts;
      ensure the repeat of past success; or
      examine the extent to which past events might have occurred differently.
      ensure the (future) avoidance of past failures.
      In science [edit]

      Scientists tend to use thought experiments in the form of imaginary, “proxy” experiments which they conduct prior to a real, “physical” experiment (Ernst Mach always argued that these gedankenexperiments were “a necessary precondition for physical experiment”). In these cases, the result of the “proxy” experiment will often be so clear that there will be no need to conduct a physical experiment at all.
      Scientists also use thought experiments when particular physical experiments are impossible to conduct (Carl Gustav Hempel labeled these sorts of experiment “theoretical experiments-in-imagination”), such as Einstein’s thought experiment of chasing a light beam, leading to Special Relativity. This is a unique use of a scientific thought experiment, in that it was never carried out, but led to a successful theory, proven by other empirical means.
      Relation to real experiments [edit]

      The relation to real experiments can be quite complex, as can be seen again from an example going back to Albert Einstein. In 1935, with two coworkers, he published a famous paper on a newly-created subject called later the EPR effect (EPR paradox). In this paper, starting from certain philosophical assumptions,[10] on the basis of a rigorous analysis of a certain, complicated, but in the meantime assertedly realizable model, he came to the conclusion that quantum mechanics should be described as “incomplete”. Niels Bohr asserted a refutation of Einstein’s analysis immediately, and his view prevailed.[11][12][13] After some decades, it was asserted that feasible experiments could prove the error of the EPR paper. These experiments tested the Bell inequalities published in 1964 in a purely theoretical paper. The above-mentioned EPR philosophical starting assumptions were considered to be falsified by empirical fact (e.g. by the optical real experiments of Alain Aspect).
      Thus thought experiments belong to a theoretical discipline, usually to theoretical physics, but often to theoretical philosophy. In any case, it must be distinguished from a real experiment, which belongs naturally to the experimental discipline and has “the final decision on true or not true”, at least in physics.
      Causal reasoning [edit]

      Generally speaking, there are seven types of thought experiments in which one reasons from causes to effects, or effects to causes[citation needed]:
      Prefactual [edit]
      Prefactual (before the fact) thought experiments speculate on possible future outcomes, given the present, and ask “What will be the outcome if event E occurs?”
      Counterfactual [edit]
      Counterfactual (contrary to established fact) thought experiments speculate on the possible outcomes of a different past; and ask “What might have happened if A had happened instead of B?” (e.g., “If Isaac Newton and Gottfried Leibniz had cooperated with each other, what would mathematics look like today?”).
      Semifactual [edit]
      Semifactual thought experiments speculate on the extent to which things might have remained the same, despite there being a different past; and asks the question Even though X happened instead of E, would Y have still occurred? (e.g., Even if the goalie had moved left, rather than right, could he have intercepted a ball that was traveling at such a speed?).
      Semifactual speculations are an important part of clinical medicine.
      Prediction [edit]
      The activity of prediction attempts to project the circumstances of the present into the future.
      Hindcasting [edit]
      The activity of hindcasting involves running a forecast model after an event has happened in order to test whether the model’s simulation is valid.
      Retrodiction (or postdiction) [edit]
      The activity of retrodiction (or postdiction) involves moving backwards in time, step-by-step, in as many stages as are considered necessary, from the present into the speculated past, in order to establish the ultimate cause of a specific event (e.g., Reverse engineering and Forensics).
      Backcasting [edit]
      The activity of backcasting involves establishing the description of a very definite and very specific future situation. It then involves an imaginary moving backwards in time, step-by-step, in as many stages as are considered necessary, from the future to the present, in order to reveal the mechanism through which that particular specified future could be attained from the present.
      In philosophy [edit]

      Whereas thought experiments in physics are intended to give us a priori knowledge of the natural world, philosophy attempts to produce a priori knowledge of our concepts:
      Philosophical and scientific investigations differ both in their methods (the former is a priori, and the latter a posteriori) and in the metaphysical status of their results (the former yields facts that are metaphysically necessary and the latter yields facts that are metaphysically contingent). Yet the two types of investigations resemble each other in that both, if successful, uncover new facts, and these facts, although expressed in language, are generally not about language (except for investigations in such specialized areas as philosophy of language and empirical linguistics).[14]
      In philosophy, a thought experiment typically presents an imagined scenario with the intention of eliciting an intuitive or reasoned response about the way things are in the thought experiment. (Philosophers might also supplement their thought experiments with theoretical reasoning designed to support the desired intuitive response.) The scenario will typically be designed to target a particular philosophical notion, such as morality, or the nature of the mind or linguistic reference. The response to the imagined scenario is supposed to tell us about the nature of that notion in any scenario, real or imagined.
      For example, a thought experiment might present a situation in which an agent intentionally kills an innocent for the benefit of others. Here, the relevant question is not whether the action is moral or not, but more broadly whether a moral theory is correct that says morality is determined solely by an action’s consequences (See Consequentialism). John Searle imagines a man in a locked room who receives written sentences in Chinese, and returns written sentences in Chinese, according to a sophisticated instruction manual. Here, the relevant question is not whether or not the man understands Chinese, but more broadly, whether a functionalist theory of mind is correct.
      It is generally hoped that there is universal agreement about the intuitions that a thought experiment elicits. (Hence, in assessing their own thought experiments, philosophers may appeal to “what we should say,” or some such locution.) A successful thought experiment will be one in which intuitions about it are widely shared. But often, philosophers differ in their intuitions about the scenario.
      Other philosophical uses of imagined scenarios arguably are thought experiments also. In one use of scenarios, philosophers might imagine persons in a particular situation (maybe ourselves), and ask what they would do.
      For example, John Rawls asks us to imagine a group of persons in a situation where they know nothing about themselves, and are charged with devising a social or political organization (See the veil of ignorance). The use of the state of nature to imagine the origins of government, as by Thomas Hobbes and John Locke, may also be considered a thought experiment. Søren Kierkegaard explored the possible ethical and religious implications of Abraham’s binding of Isaac in Fear and Trembling Similarly, Friedrich Nietzsche, in On the Genealogy of Morals, speculated about the historical development of Judeo-Christian morality, with the intent of questioning its legitimacy.
      An early written thought experiment was Plato’s allegory of the cave.[15] Another historic thought experiment was Avicenna’s “Floating Man” thought experiment in the 11th century. He asked his readers to imagine themselves suspended in the air isolated from all sensations in order to demonstrate human self-awareness and self-consciousness, and the substantiality of the soul.[16]
      Possibility [edit]
      The scenario presented in a thought experiment must be possible in some sense. In many thought experiments, the scenario would be nomologically possible, or possible according to the laws of nature. John Searle’s Chinese room is nomologically possible.
      Some thought experiments present scenarios that are not nomologically possible. In his Twin Earth thought experiment, Hilary Putnam asks us to imagine a scenario in which there is a substance with all of the observable properties of water (e.g., taste, color, boiling point), but which is chemically different from water. It has been argued that this thought experiment is not nomologically possible, although it may be possible in some other sense, such as metaphysical possibility. It is debatable whether the nomological impossibility of a thought experiment renders intuitions about it moot.
      In some cases, the hypothetical scenario might be considered metaphysically impossible, or impossible in any sense at all. David Chalmers says that we can imagine that there are zombies, or persons who are physically identical to us in every way but who lack consciousness. This is supposed to show that physicalism is false. However, some argue that zombies are inconceivable: we can no more imagine a zombie than we can imagine that 1+1=3. Others have claimed that the conceivability of a scenario may not entail its possibility.
      Other criticisms [edit]
      The use of thought experiments in philosophy has received other criticisms, especially in the philosophy of mind. Daniel Dennett has derisively referred to certain types of thought experiments such as the Chinese Room experiment as “intuition pumps”, claiming they are simply thinly veiled appeals to intuition which fail when carefully analyzed. Another criticism that has been voiced is that some science fiction-type thought experiments are too wild to yield clear intuitions, or that any resulting intuitions could not possibly pertain to the real world. Another criticism is that philosophers have used thought experiments (and other a priori methods) in areas where empirical science should be the primary method of discovery, as for example, with issues about the mind.

    3. Sorry Anon, I tried to read it all but couldn’t. My loss. What I did read though was very interesting.

  26. I think Richard’s answer makes sense. Here’s how:
    I assume each of the 3 men would have a natural instinct to want to stay alive. When the first person has fired into the air, he has lost a bullet, therefore becomes harmless. The only person that is now a threat to the second person is the third person who still has bullet that has not been fired. So to eliminate the threat, the second person would shoot the third person. Actually, two people will be left standing, that being the first and the second person. That’s how the first person ensures his survival.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s