Trowels, Grids and Guesses: A Probability Dig Beneath Leicester

Leicester has a habit of putting history under practical things. In 2012, archaeologists searching for the lost choir of Greyfriars Priory lifted a car park surface near New Street and found Richard III. It is a brilliant story — bones, a curved spine, a Leicester Cathedral reburial in 2015 — but from a maths point of view, the best bit is not the crown or the skeleton. It is the uncertainty.

The search was not a lucky dig. It was a sequence of guesses, maps, samples and updated beliefs. That makes it a near-perfect hook for a problem-solving lesson on probability, sampling and Bayesian reasoning.

Start with a hunch, not a certainty

Before anyone broke tarmac, the team had a prior belief. Historical documents pointed to Greyfriars Priory. Maps and records suggested the choir, and therefore a possible royal grave, lay somewhere under what had become a council car park. Nobody knew the exact square metre. They had a ranked set of possibilities.

In Bayesian language, that starting belief is the prior. It is not a wild guess; it is what you think before the new evidence arrives, based on what you already know. Then you gather evidence — a trench, a wall, a fragment of tile — and ask how likely that evidence would be if your idea were true compared with if it were false. The result is a posterior: a revised belief.

You do not need the formal formula to use the idea. The classroom version is simply: start with a sensible guess, look at the evidence, then change your guess by the right amount.

Why a small trench can speak for a big site

Archaeologists rarely dig an entire site. They sample. A test pit is a small window into a large area, and the maths of sampling is what makes that window useful.

Imagine two possible worlds. In World A, the grave lies in the area you are testing. In World B, it does not. If you dig a trench and find nothing, that absence is much more informative in World A than in World B — but only if your trench was in the right place and your search was good enough to spot the grave. A trench that misses the target does not prove there is no target. This is the false-negative problem, and it is exactly the sort of careful thinking we want students to practise.

That is why the Greyfriars dig is more than a treasure hunt. It is a lesson in evidence quality. A small sample can tell you a lot, but only when you are honest about what it can and cannot rule out.

The Leicester grid game

Here is a simple activity for a classroom, a maths club or a kitchen table. It takes about 20 minutes and needs very little kit.

You need: a large sheet of paper marked with a 5-by-4 grid, one hidden token (a coin, a counter or a picture of a king), and a few clue cards.

Set-up: tell students the grid is a simplified Greyfriars car park. One square hides the royal grave. Before any clues, ask them to shade each square with a probability. They should not simply colour all squares equally. A square near the supposed choir line might deserve more belief than one near the sandwich van.

Clue round: read out two or three clues, such as:

• The grave is not in the top row.
• The grave is in an even-numbered column.
• The grave is within two squares of the old choir wall.

Students update their shading after each clue. The point is not to get the exact number right. The point is to explain why the shading changed.

Sampling round: instead of digging every square, each team chooses one test square. Reveal whether the token is there. If it is not, the team must update again — but they must also say what their empty trench does and does not prove.

Final dig: teams choose one last square and compare their reasoning. The winning team is not necessarily the one that finds the king. It is the one that best explains how its beliefs changed.

From car park to classroom

Bayesian thinking is not an extra topic bolted onto GCSE probability. It is a habit: say what you think, say how sure you are, and say what evidence would change your mind. That habit fits neatly into problem solving, whether students are estimating a population from a sample, checking a claim in the news or deciding whether a suspiciously quiet bus stop means the bus has already gone.

And Leicester has a genuine claim to this story. The king in the car park was found because people combined historical knowledge with careful sampling and a willingness to revise their plans. In 2026, that is still a very good model for a maths lesson: dig where the evidence points, keep the uncertainty visible, and update honestly when the ground answers back.