Walking Maths in Coventry

Welcome to (virtual) Walking Maths in Coventry! Right now, various mathematicians are in Coventry looking for clues. With a little help from Google Street View and a few photos, you can enjoy this puzzle hunt too.

There is a (virtual) locked box at mscroggs.co.uk/coventry-trail/box. Your challenge is to work out the code for the combination lock on the box to get to the prizes inside. The code is a four-digit number.

During the trail, you will discover five clues to the code. You will need to find information around Coventry and solve some puzzles to reveal each clue. You may wish to use a calculator for some of the puzzles.

The trial starts at Coventry Transport Museum. Head outside into Millennium Place. A little to your left, you should see a building with crenellations—it's Swanswell Gate, part of Coventry's city walls. Head towards Swanswell Gate, and you'll find yourself in some gardens named after a lady. The year in which these gardens opened to the public is \(a\).

15⁴ is equal to 50625. The hundreds digit of 15⁴ is 6. The difference between the first and second digits of the code is the hundreds digit of \(15^a\).

Go back out of the gardens and head left towards Sainbury's. Cross the road by Sainsbury's then head down Priory Place to the left of the BBC building.

When you arrive in a plaza full of restaurants head up the stairs or ramp. Walk in the same direction as you entered the plaza, then turn left past The Priory Undercrofts. Head straight on until you reach Priory Street.

Turn right onto Priory Street and walk alongside the cathedral until you reach St Michael's Avenue, where the cathedral's entrance is located. Turn right and head up the stairs or ramp.

The cathedral was almost completely destroyed during the Coventry Blitz in 1940 during World War II. At the top of the stairs, you'll see the modern cathedral to your right and the ruins of the older cathedral to your left. One of the foundation stones of the modern cathedral was laid by Queen Elizabeth. The year in which it was laid is \(b\).

If you write the numbers from 1 to 10000 in a huge triangle like this:

... then 11 is written directly below 5. The second digit of the code is not the tens digit of the number written directly below \(b\).

Head along St Michael's Avenue then straight on past Holy Trinity Church. After a while, you'll arrive at a replica of Coventry Cross.

The original Coventry Cross stood from 1544 until the 1770s when it was demolished. The current replica was in Coventry between 1976 and 2019 before being removed then put back (in a slightly different location) in 2023. Read the information on Coventry Cross. The year in which Henry VI first visited Coventry is \(c\).

The area of largest quadrilateral that fits inside a circle with area 2π is 4. The difference between the first and last digits of the code is the thousands digits of the area of the largest dodecagon that fits inside a circle with area \(c\)π.

Head to the right along Broadgate. When you reach Broadgate Square, head towards the statue of someone riding a horse---even though she's riding a horse near a cross, she's probably not the same fair lady who rode a cock horse to Banbury Cross with rings on her fingers and bells on her toes who has music wherever she goes. The year in which this statue was presented by WH Basset Green to his fellow citizens is \(d\).

There are 10 dominoes that can be made using the numbers 0 to 3 (inclusive):

The sum of all the numbers on all these dominoes is 30.

The difference between the largest and smallest digits in the code is the units digit of the sum of all the numbers on all the dominoes that can be made using the numbers 0 to \(d\) (inclusive).

Head back to Coventry Cross, and head along Trinity Street (the only road from the cross that you've not on been yet). Wave hello to the Flying Standard where we met after dinner last night, then turn left along Ironmonger Row. Follow the road to the right as it changes its name to Cross Cheaping then The Burgess. If you're a comic book fan, quickly pop into Forbidden Planet before continuing the trail.

When you reach a crossroads, look for the Old Grammar School. The year in which Sir William Dugdale left the school is \(e\).

The number \(n\) has \(e\) digits. All of its digits are 9. The last digit of the code is the hundreds digit of the sum of all the digits of \(n^2\).

You should now have enough information to work out the code. Head to mscroggs.co.uk/coventry-trail/box.