Math Puns Explained

There are only 10 types of people in the world —
those who understand binary, and those who don't.

This joke relies on the fact that mathematical expressions, just as expressions in natural languages, may have multiple meanings. When multiple meanings are available, puns are possible. In this case a pun is made using the expression 10. For non-mathematicians or non-computer programmers 10 almost always refers to the number ten. However, in binary, the expression 10 means the number two. Thus the joke says that there are only two kinds of people, those who understand binary, and those who don't. However, those who do not understand binary will certainly not get the joke. This joke is only feasible in written form; when speaking a binary number aloud, "10" would be phrased as "one zero" or simply "two", rather than "ten".

There are only 10 types of people in the world —
those who understand binary, those who don't, and those who understand Gray code.

In Gray code, "10" would be phrased as "one zero" or simply "three", rather than "ten", adding another layer of subtlety to the joke.

A self-deprecating version is as follows:

There are only 10 types of people in the world —
those who understand binary, and those who get laid.

The following joke refers to the original joke:

There are only 10 types of people in the world —
those who understand ternary, those who don't, and those who mistake it for binary.

A similar joke may be played by asking the question:

If only DEAD people understand hexadecimal, how many people understand hexadecimal?

In this case, DEAD refers to a hexadecimal number (57005 base 10), not the state of being no longer alive.

Another pun using different radices, sometimes attributed to computer scientists, asks:

Why do mathematicians think Halloween and Christmas are the same?
Because 31 Oct = 25 Dec.

The humor lies in the fact that Halloween occurs on October 31 and Christmas occurs on December 25, thus equating "oct" in October and octal, and "dec" in December and decimal. (This one is also often attributed to computer scientists: Real programmers confuse Halloween and Christmas — because dec(25) = oct(31).)

Another joke involving counting is:

There are three kinds of people in the world: those who can count, and those who can't.

This implies, of course, that the person making the statement is the latter.

Almost everyone knows the trite line: "Why did the chicken cross the road?" "To get to the other side". A mathematical variation follows as: "Why did the chicken cross the Möbius strip?" This joke relies on the audience knowing that since the Möbius Strip is a surface with only one "side" (i.e., one "edge"), anyone trying to give the typical answer will realize its impossibility. The answer is sometimes also given as "To get to the same side", with the same rationale.