1⁷ + 7⁷ + 4⁷ + 1⁷ + 7⁷ + 2⁷ + 5⁷ = 1741725

Each term in this equation contains each of the nine digits once:

2 is the only even prime.

But the total number of primes is infinite.

Therefore the probability that a given prime number is even is 1 over infinity, or zero.

Hence it’s impossible for a prime number to be even — and 2 does not exist.

5⁵ + 4⁵ + 7⁵ + 4⁵ + 8⁵ = 54748

Let’s say that the densest human head of hair contains 200,000 strands, and that the human population is 6 billion. That means there’s a group of at least 30,000 people today who have precisely the same number of hairs on their heads.

Do you see why?

Suppose the earth were a perfect sphere and you fitted a belt around its equator.

The belt would be 40 million meters long. If you now increased its length by a mere 5 meters, how high would it ride above the earth’s surface?

The answer, surprisingly, is 0.8 meters — well above the current limbo record.

Look! Canceling exponents works even in algebra:

1634 = 1⁴ + 6⁴ + 3⁴ + 4⁴