School-Safe Puzzle Games

3 Men by the Seaside

Anderson, Biggs, and Carpenter were staying together at a place by the seaside. One day they went out in a boat and were a mile at sea when a rifle was fired on shore in their direction.

It seems that Anderson only heard the report of the gun, Biggs only saw the smoke, and Carpenter merely saw the bullet strike the water near them. Now, the question arises: Which of them first knew of the discharge of the rifle?

Bilbao provides this reasonable short puzzle to start the week : )

Also from Bilbao: the 12 Dots problem

21 Comments to “3 Men by the Seaside”

  1. RK | Founder | Profile


  2. Obiwan | Profile

    Hmmm…this happened one day and the picture is indicates daytime…
    1. Smoke suggests bullet is subsonic–hence sound of bullet should arrive before bullet.
    2. One assumes smoke is essentially visible just after bullet leaves muzzle.
    3. Bullet, sound wave and smoke all leave muzzle at approximately the same time.
    4. Appreciation of smoke should be evident as soon as light reaches the eye (moving at 186,000 miles/sec) but this assumes one can appreciate a muzzle blast from a mile away.

    The statement says “Biggs only saw the smoke”–so it must be Biggs.

  3. Bobo The Bear | PUZZLE MASTER | Profile

    This one is sure to generate some controversy. I think that a rifle bullet travels faster than the speed of sound, but what I don’t know is how quickly a smoke cloud from a rifle grows in size to the point that it would be visible from a mile away. I doubt that it’s instantaneous.

    My guess: the bullet strike is first, the sound of the discharge is next, and the sight of the smoke is last.

    This would be a cool one for MythBusters!

  4. Shawn | PUZZLE GRANDMASTER | Profile

    So the questions we must first answer are,
    Does a rifle bullet travel faster than sound?
    Does the smoke come from a rifle immediately upon firing, or is their a delay?

  5. Shawn | PUZZLE GRANDMASTER | Profile

    Internet says that even an old rifle bullet travels at 800-1000m/s minimum. Average speed over a 1-mile distance would be lower, but still higher than the 340m/s speed of sound. So the bullet arrives before the sound, and Anderson is eliminated.
    Sound : (1610m)/(340m/s) = 4.7 seconds
    Bullet: (1610m)/(1000m/s) = 1.6 seconds

    Now, one could argue that Carpenter, upon seeing the splash made by the bullet entering the water, would have no idea that it was a bullet and would probably be much more likely to assume that a fish had surfaced or a bird had dropped something. Why should he suspect that someone was shooting at him?? I will therefore assume that Carpenter “knew of the discharge of the rifle” simply by seeing the splash, even if he didn’t immediately know that it was caused by a bullet.

    Now the smoke. Old muskets such as used in the 18th and 19th centuries used open powder that issued a large cloud of smoke as soon as it was ignited, so quickly that it would appear instantaneous. Today’s rifles produce very little visible smoke, certainly not visible from a mile away. We must assume that either it is an old-style rifle (as the vintage of the picture suggests) or that Biggs is a liar. I will assume the former.
    (1610m)/(3×10^8m/s) =~0 seconds

    If the smoke appeared in less than 1.6 seconds (in a large enough cloud to see from a mile away, as Bobo pointed out), AND if Biggs happened to be looking at the exact point on shore at the exact time that the rifle was fired, then the smoke would be seen before the bullet struck the water. It must be noted, however, that Biggs could have turned around 5 seconds after the shot and only then noticed the lingering puff of smoke.

    All of which leads me to believe that the order of recognition is Biggs, then Carpenter, then Anderson.

    See smoke, see bullet, hear rifle.

  6. yumyum36 | Profile

    Whoever shot the gun…

  7. RK | Founder | Profile

    Bilbao would be impressed, Shawn!
    Someone should hire you to review the Zapruder film ;)

  8. Shawn | PUZZLE GRANDMASTER | Profile

    You should post a puzzle with nothing but the Zapruder video and ask for a solution. If any group could come up with some inventive possibilities, it’s this bunch!

  9. Mashplum | PUZZLE MASTER | Profile

    The gun would have been aimed high – maybe 45 degrees – to make the bullet travel a mile. This cuts the horizontal component of velocity by about 70%. Then there is drag to consider. Without knowing the exact velocity and the drag coefficient of the bullet it would be hard to determine how long it took for it to splash the water. It could possibly take longer than the sound. The sight of the smoke travels at light-speed, but it would be very hard to see it from a mile away. If you held a ruler at arm’s length, a man one mile away would appear smaller than a millimeter. I would be willing to say it is impossible to see the smoke from a single rifle shot at that distance with the naked eye.

  10. Mashplum | PUZZLE MASTER | Profile

    Here is a pic I made to illustrate the problem. Stand 30 feet from your computer and try to see the smoke.

  11. Mashplum | PUZZLE MASTER | Profile

    Here is a pic I made to illustrate the problem. Stand 3 feet from your computer and try to see the smoke.

  12. Shawn | PUZZLE GRANDMASTER | Profile

    Point taken, Mashplum. Assuming that the relative distances in your picture are accurate, and also assuming that the gun did not make a much larger cloud than the one in your picture, then it would be very improbable that Biggs would see the smoke unless he was looking directly at the spot and anticipating that the shot would be fired, so it’s very unlikely that Biggs would be the first to know about the shot, and more likely that he saw the smoke cloud later, after the others realized something strange was happening.

  13. Shawn | PUZZLE GRANDMASTER | Profile

    Unless Biggs WAS looking at an exact spot on the shore because he WAS anticipating the shot because it WAS a conspiracy as RK picked up on a few comments ago.

    Now the only question remaining is, who was Biggs’ accomplice trying to shoot, Anderson or Carpenter?

  14. Mashplum | PUZZLE MASTER | Profile

    I believe the smoke cloud could get bigger than shown in my picture, but not until several seconds later. The size of the cloud at the time of firing would be small but it would grow as it dissipates. Of course, as it gets larger, it becomes less dense too. Biggs would have a better chance at seeing the flash. If the shooting occurred after dark, I would give Biggs the edge.

  15. Mashplum | PUZZLE MASTER | Profile

    BTW, if anyone wants to check the math on my image, the large soldiers are 20 pixels tall (0.2 in) and the small ones are 4 pixels (0.04 in). IRL the soldiers would be 70.4 in.

  16. joe | Profile

    may I ask for the correct answer on this one Señor Bilbao?

  17. Hex | PUZZLE MASTER | Profile

    I’ll give my take:

    – Muzzle velocity is quite different than impact velocity. The farther the bullet travels, the lower its velocity is.

    – Since the rifle produced smoke, it must be using black gunpowder, the properties of which are quite different from modern smokeless powder.

    – The bullet drops vertically with distance.

    – The smoke cloud will be barely visible from a mile away. Biggs (Bunny?) must have been eating a lot of carrots :D . I assume he was using binoculars and following the man holding the rifle.

    – Smoke, sound and the bullet get out of the muzzle at the same instant. Hence the smoke will be noticed first as light is the fastest.

    – Remains to check if black gunpowder rifle bullets travel at supersonic or subsonic speeds as an average over a mile’s distance, that is if its bullet ever reaches a mile.

  18. neutrondisciple | Profile


  19. SirJack | Profile

    Ok, my answer is NONE of three.
    Let’s analyze the text of the puzzle.
    It starts saying that “It seems that…” so the subsequent sentences are not affordable… but let’s go on… then says that “Anderson only heard the report [I mean the noise] of the gun”, so Anderson only heard a big instant noise that could be justifyied by a lot of other reasons (a car with problems, kids playng with small explosives, and so on), so Anderson does not know if a rifle has shot or not.
    Then “Biggs only saw the smoke” and a smoke is only a smoke.
    Last “Carpenter merely saw the bullet strike the water near them”. What does it mean? It means that Carpenter only sees someting in the sea surface
    that could be caused maybe by a fish.
    Now, the answer arises: none of them knew of the discharge of the rifle.

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