Hide a Pigeon Pair for Verkle Tree Cryptography

Vitalik Buterin needs to hide an extra pigeon somewhere to solve some other big brain moon math called Verkle Trees for blockchains.

We’re talking about pigeons because of the so-called pigeonhole principle — where you can only fit N pigeons into N holes. If we added 1 more, to have N+1 pigeons, we’d need to stuff 2 into 1 hole (hey, stop goofing off). In the case of this problem, we want to stuff 2 in 1 hole, but we want people to be beyond astronomically unlikely to ever find the hole with 2 pigeons in it.

He has 2 huge sets of pigeons, 2²⁵⁶, which is about as many as the atoms in the universe. Some parks have many pigeons, but this is getting ridiculous.

The Problem

Any formula that singles out how to hide the extra pigeon will be visible.

Impossible?

A solution may not exist, given the requirements.

If it did, it’d perhas solve a whole class of problems called PPAD.