The Centipede Theorem

Warning: this theorem may cause dizziness, vertigo, or spontaneous outbursts of singing.

Statement of the Theorem

Let S be a set of n legs, where n > 2. Then there exists a centipede of length n-2, such that the sum of the lengths of its legs is exactly 1000 times the number of its legs.

Proof

Assume that the centipede has k legs. Let the lengths of its legs be a1, a2, ..., ak. Then the sum of the lengths of its legs is a1 + a2 + ... + ak. By a simple rearrangement, this sum is equal to (a1 + a2 + ... + ak) + 0 + 0 + ... + 0.

Now, consider a single leg of length 1000k. Then the sum of the lengths of all k legs is equal to 1000k, as desired.

This completes the proof.

Corollaries

• Centipede Theorem 1: The centipede is always a multiple of 100
• Centipede Theorem 2: The centipede may or may not be a multiple of 100
• Centipede Theorem 3: The centipede is always a multiple of 1000, but only if it's a Tuesday

References

Boris the Brute, "The Centipede Theorem: A Study in Unconventional Math", available now!