Identical Twins

Alice and Eve are identical twin sisters. One always lies and the other always tells the truth, but we don't know which is which. We ask one of them "Is Alice the one that always lies?" and she replies "Yes." Did we speak to Alice or Eve? Click below to see the answer.

We spoke to Eve. A person who always lies or always tells the truth cannot admit that they are a liar, so Alice could not have answered "Yes" to that question. (Note that we still don't know which sister is the liar and which is the truth teller.)

Counting Socks

All my socks are red except two. All my socks are white except two. All my socks are blue except two. How many socks do I have? Click below for the answer.

Oddly, I only have three socks. Don't let the fact that socks normally come in matching pairs distract you. No other number satisfies all three conditions above.

Circumnavigation

From 1519 until 1522, Ferdinand Magellan's Victoria was the first ship to successfully circumnavigate the globe. (Magellan himself did not survive the entire voyage.) Can you tell me which part of the ship traveled the greatest distance? Click below for the answer.

If you remembered the Rope Around the Earth puzzle I posted a few months ago, you probably got this one pretty quickly. Since the world is roughly spherical, the tip of the tallest mast of the ship would have traveled the greatest distance in sailing around the globe. Imagine if a boat sailed in a perfect circle around the equator. The part of the boat deepest under water (the keel) would create a smaller circle than the tip of the mast several feet above the water, so the tip of the mast travels the greatest distance during the voyage.

Replica of the Victoria, Photograph by Gnsin - Own work, CC BY-SA 3.0

50 factorial

50! = 30414093201713378043612608166064768844377641568960512071337804000

Without doing the full computation, can you tell whether the above statement is true or false? Click below for the answer.

You can probably guess that the statement is false, otherwise it wouldn't be much of a puzzle. The reasoning, though, is that the factorial for 50 must include the factors 10, 20, 30, 40, and 50, so it must end in at least five zeroes. The value above ends in only three zeroes, so it cannot be correct. (The correct value is 30414093201713378043612608166064768844377641568960512000000000000.)

The Missing Fish

Two fathers took their sons fishing. Each man and his son caught one fish, but when they all returned to camp they only had three fish. None of the fish were eaten, lost, or thrown back. How could this be? Click below to see the answer.

There were only three people on the fishing trip. One man was the father and grandfather of the other two.