The riddle
What Has a Head and a Tail but No Body?
Two sides, no body
Heads is the side of a coin that shows a portrait, usually a person's head. The other side is called tails. A coin is flat, so it has the two sides the riddle names and no body between them. The formal names are obverse and reverse, and the obverse is the face that carries the main design.
Is a flip fair?
Flipping a coin is the usual way to decide who goes first, and it is treated as an even chance. Mathematicians Persi Diaconis, Susan Holmes and Richard Montgomery argued in a 2007 paper that a coin caught in the hand is slightly more likely to land on the face that started up. A 2023 study of 350,757 flips found that coins landed on their starting side about 50.8 percent of the time. That is far too small a difference to notice in a few flips.
Coins with a head on them
The United States one-cent coin has carried Abraham Lincoln's head since 1909. Dimes and quarters have ridged edges, which is the nearest a coin comes to anything beyond its two faces. The riddle depends on that: a head and a tail are the two sides of a flat disc.
Seen from the other side
Heads and tails are opposite faces, so they can never both show at once. That is also why the riddle stops at "no body": a coin's thickness is just its edge.