Challenge #13 – J. Bozo

We’re back with another challenge! This is in collaboration with Agent Venture who provide amazing online escape room experiences – make sure you check them out!

The Challenge

Agent Venture needs your top-notch bank robbery skills to help bring J. Bozo to justice for their numerous crimes.

The incriminating files against J. Bozo are locked behind a room with a keyboard and a 3×3 digital grid with letters on it… The passcode is in the form of a pattern which only a few employees know, can you work out what the pattern-passcode of the grid is?

The Solution

Let’s start by looking at Employee 1, we can see that there are multiple ways we can reach the typed passcode. See the images below to see some of the possible methods. How many ways of getting B, A, B, A, B can you find from Employee 1’s grid?

Similarly for Employee 2, we can see that there are also multiple ways in which we can reach the typed passcode. However, we can deduce that the pattern must start on the middle right square since there is no other starting point for C,C,B in a row (C,C,B,A,B).

Lastly, for Employee 3, there are also multiple ways of reaching the typed passcode C, A, C, B, C.

Using the information we gathered from Employee 2, we can deduce that if we start on the middle right square using Employee 1’s grid, then the next move is to go down to the bottom right square. If we instead try to go up to the top right square, then we reach a dead-end and end up with B, A, C even though the passcode for Employee 1 starts off as B, A, B (B,A,B,A,B).

It is still ambiguous what the next part of the pattern is by looking at the grids for Employee 1 and Employee 2. However, looking at the grid for Employee 3, we can see that the pattern must go through the middle square to get the last part of the pattern-passcode.

Putting all this information together and overlaying the pattern over the grid, we can deduce that the solution is F, I, H, E, D!

How did you do? Comment below how you reached the solution!

E08: How 2 be a snake

Imagine you and a stranger are paired together for a little game. Now there’s some money up for grabs and you’re both given 2 choices; Share or Snake.

If you both share you both win £15 each.
If one of you shares and one of you snakes, the snake will win £50 leaving the person who chose share with nothing.
If you both pick snake, you both leave with nothing.

Would you pick ‘snake’ in the hopes of taking a bigger prize for yourself, or would you pick ‘share’ to share a smaller prize!? What would you do? What should you do? And why should we even care?
In this episode, which is also the season finale, Bia shares some introductory game theory with Zoey by discussing:

The social-media experiment they both conducted through Instagram: “Snake or Share”
The Prisoner’s dilemma (which is the original problem)
The Traveller’s dilemma.

Acting like a “snake” i.e. picking the “dominant strategy” may give you control leaving you less susceptible to exploitation, but is it always the most profitable strategy? And what about the long-term implications of this?

Sodosage’s Instagram (poet): @sodosage

Challenge #12 – The Blueprints

The Challenge

Finally, you have your hands on the blueprints to the bank. You can see that on the blueprints there are only certain routes which you can take in order to avoid triggering the security alarms at 3:23AM (prime bank robbing time).

You need to plan your route carefully to get to the vault as quickly as possible and avoid detection. Luckily, someone has added the number of footsteps it takes along the routes on the blueprints!

First you need to go into the reception cabinet to obtain the keys to the HR office which contain employee records. Inside the records you will find the password to the computer of your accomplice who works in foreign exchange. Your accomplice has left you a key to access the cupboard by the Business Analyst’s desk. You need to find a file containing information about the top-secret floor – including the passcode to the vault.

Can you find a route that takes no more than 217 steps?

The Solution

Did you manage to find a solution under 217 steps? You’ve just solved a graph theory problem! Graph theory is the mathematical study of graphs which consist of vertices (or nodes, such as the Coffee Machine in the maze) which are connected by edges.

This problem in particular is known as the shortest path problem – we want to find a path between two nodes so that the total is minimised!

See the image below for the shortest path which takes exactly 217 steps.

The shortest route (with a total of 217) is: Entrance, Reception Desk (12), Reception Cabinet (9), Fish Tank (18), Microwave1 (7), Recruitment Materials (16), Employee Records (6), Training Materials (18), Head of HR Seat (10), Foreign Exchange (25), Microwave2 (36), Fridge (8), Frontend Engineers (11), Business Analysts (3), Data Analysts (19), Drinks Machine (14), VAULT (5).

E07: How 2 create a dating app

How do dating apps work? And what are your thoughts on them? In this episode, Zoey shares how collaborative filtering works in dating apps such as Tinder, but also in Amazon. Bia shares how Hinge uses the Gale-Shapley algorithm (whilst butchering the pronunciation) to find your most compatible match. They discuss thoughts people shared via Instagram.

Further details of the maths and algorithms are shared via Instagram!

Time stamps:
0:47 – Collaborative filtering
13:55 – Gale Shapley algorithm
19:04 – Are dating apps are good/bad thing? Thoughts of Instagram followers
28:48 – Who do dating apps favour/ hinder? Thoughts of Instagram followers & some personal stories

Useful Links:

Hinge uses Gale-Shapley algorithm
Judith DuPortail’s article
Interracial dating online

E06: How 2 illustrate a scientist with Nina Chhita

In light of International Women’s Day 2021, Zoey and Bia interview Nina Chhita, a medical writer based in Canada. Nina brings together art and science by illustrating trailblazers in science who happen to be women. 

00:10 Introduction
02:09 Quick fire quiz
03:15 What does it mean to be a medical writer?
05:31 Did you always want to study biology when you were younger?
08:10 Who were your role models growing up?
11:39 Which blue plaque story led to @science.unhinged and @nina.draws.scientists?
14:59 What was it about Rosalind Franklin that drew you to her story?
6:15 How do you get inspiration for the scientists you illustrate now?
18:26 How easy is it to find misinformation about less well-known women?
20:30 Which scientist you’ve illustrated has been most fascinating to you?
23:42 Has anything surprised you on this journey of science communication?
26:26 What are ways we can feature women in science to be more mainstream?
32:40 What would you change about the current curriculum to encourage girls to take more STEM-based subjects?
33:40 How much more progress do we need in the future and how do you think we can get there?
35:34 What makes a good scientist in your opinion?
37:45 What is planned next for nina.draws.scientist?

Connect with Nina Chhita on Instagram @nina.draws.scientists and on Twitter @Nina_Chhita.

E05: Q&A

In this episode, Zoey and Bia answer questions submitted by listeners. These include what inspired them to make the podcast, Instagram page and blog, why a common person should learn maths, and how hard it is to get good at it.

00:36 What inspired you to make this page and podcast?
02:00 Who are we?
02:49 How did we meet?
03:37 What inspired you to take maths at university?
04:38 What advice would you give yourself if you could go back in time 10 years?
05:25 What advice would you give to young girls who want to pursue STEM (Science, Technology, Engineering and Mathematics)?
06:30 Why do you think a common person should learn maths?
09:39 How hard is it to get good at maths?
12:40 What is missing from elementary school maths syllabus that would make maths more fun?
14:13 Are mathematical models underrated or overrated?
16:37 Do you have any maths book recommendations?
18:10 Does it annoy you that people think you are men online?
20:18 From your experience, what have you learnt about communicating maths ideas online?

Useful links:

E04: How 2 lie with zombie statistics

Zoey and Bia discuss what zombie statistics are, why it’s hard for zombie statistics and facts to die and whether it is right for a wrong statistic to be cited even if it produces positive effects.

00:15 – Lies, damned lies and statistics
01:48 – Zombie statistics definition
Quiz and answers discussion
03:52 – Zombie stats or facts quiz
05:45 – Zombie stat/fact #1 – One in four people will suffer from mental illness/ depression in their lifetime
09:18 – Zombie stat/fact #2 – You need to drink eight glasses of water a day
12:18 – Zombie stat/fact #3 – People use only 10% of their brains
14:22 – Zombie stat/fact #4 – You need to walk 10,000 steps a day to stay healthy and fit
19:05 – Zombie stat/fact # 5 – The ban of plastic straws will massively reduce plastic waste in our oceans
General discussion
26:26 – Discussion on why it’s hard for zombie stats/facts to “die” – beneficial information to people/companies and confirmation bias?
30:37 – Is it okay for a statistic to be wrong even if it has a positive effect?
33:45 – Making sure you understand the entire story of the statistic and taking it with a pinch of salt
35:29 – Conclusions

Useful links:
Adult Psychiatric Morbidity in England – 2007, Results of a household survey
Medical Myths”
Dirty Streaming: The Internet’s Big Secret

E03: How 2 rig an election

Bia and Zoey discuss some of the key mathematical concepts in voting, focusing on political elections in some Western countries, as well as Brexit.

0:15 – Introduction on the voting system in the UK, with an example
4:27 – Condorcet’s paradox 6:00 – The French system
6:44 – The Australian system – Preferential/Alternative voting
7:42 – What defines a good voting system?
9:43 – How do we balance a good voting system with one which everyone understands
Arrow’s Impossibility Theorem & Instagram poll
11:40 – Arrow’s Impossibility Theorem
13:46 – Independent voting systems where Arrow’s theorem doesn’t apply.
15:00 – Instagram poll discussion: Tactical voting vs Voting for who you want
17:31 – Protest voting vs voting for who you want
20:20 – When it would be worth strategically voting “mathematically”
Brexit21:22 – Zoey exposing Bia as a “Remoaner”
22:50 – How Bia think the referendum should have been done. General discussion
24:05 – Have you ever not voted?
26:12 – Should 16 year olds be allowed to vote? 2
27:29 – Accessibility in a voting system
The future of voting
27:54 – The future of voting
28:52 – The issues with a voting system which takes too long (NP-hard/ NP-complete)
30:00 – Dodgson’s voting method (Lewis Carroll = Charles Dodgson)
32:52 – Final thoughts

80% of voters are strategic: “Counting Votes Right: Strategic Voters versus Strategic Parties, Filippo Mezzanotti and Giovanni Reggiani”

Black History Month 2020

Here in UK, October is Black History Month. To celebrate, we posted a three-part mini series on our Instagram.

1. Mathematics in Timbuktu

Part one dives into the Mathematics in Timbuktu. The recently rediscovered Timbuktu manuscripts (dating back to the 13th century) demonstrate the continuous knowledge of advanced mathematics and science in Africa well before colonisation. They understood trigonometry, they created algorithms and they were advanced in astronomy!

2. Black Mathematicians

For part two of the mini series, we mention a few notable Black Mathematicians.

  • Thomas Fuller (1710-1790) was an African-born slave in America known as the Virginia Calculator for his extraordinary powers in arithmetic.
  • Marta Euphemia Lofton Haynes (1850-1980) is the first Black woman in the US to earn a PhD in Mathematics in 1943.
  • Jesse Ernest Wilkins Jr. (1923-2011) entered the University of Chicago at 13 years old and became the youngest ever student at that university.
  • Katherine Adebola Okikiolu (1965-present) is the first Black person to receive a Sloan Research Fellowship. (43 fellows have won a Nobel Prize, and 16 have won the Fields Medal in Mathematics)

3. Ancient African Mathematics

For our third and final post, we discuss the first mathematical instruments known to us – the origin of these fascinating ancient relics is African!

  • The Ishango Bone 🦴 (2,000 BC): This bone has 3 columns with different markings on them in clusters.
  • The Lebombo Bone🦴 (30,000 BC): This bone has 29 markings on it believed to be linked to a lunar cycle.

The purpose behind the creation of these relics is still disputed. According to certain historians, (e.g. Museum of Natural Sciences, Brussels, where the Ishango bone is presented), it is believed that the people of Ishango knew about prime numbers. However, some mathematicians say that the presence of prime numbers on the bone is a coincidence and that they were actually using the bone as a counting tool. Either way, it is fascinating that people over 35,000 years ago were using maths in some way – possibly before the invention of numbers!

Both of these bones were made on baboon fibulas. The baboon was a symbol of the Ancient gods of the moon which suggests an ancient connection between baboons, the moon, time, and maths.

Did you enjoy this? Make sure you’re following us on instagram @how2robabank!

E02: How 2 predict grades badly…

In this episode, we discuss some of the mistakes that Ofqual made in their algorithm, how using “complicated” maths is not necessarily better, and share some anecdotes of their experiences with teachers and dealing with (un)conscious bias.

00:20 – Introduction
01:54 – Initial thoughts
02:42 – Mistake #1 – Their approach
04:43 – Mistake #2 – Data leakage
05:15 – Mistake #3 – Emphasis on the rank
06:57 – Mistake #4 – Ignoring outliers
08:31 – Mistake # 5 – No peer review
09:16 – Mistake #6 – Too precise
11:14 – Mistake #7 –Disregarded unconscious bias.
12:53 – Mistake #8: Education system in the UK.
13:30 – Ofqual considered edge cases – (almost a positive thing!)
15:00 – How we might have handled this situation
17:39 – Another example of algorithmic bias – Accounting system the Post Office used.
18:53 – Challenge: “Prison Break”. This based on “Liar’s paradox” attributed to Epimenides (amongst many other philosophers). For more challenges, presented in a more visual manner, check out our Instagram.
25:52 – Anecdotes of experiencing bias from teachers.

Useful links:
Ofqual’s reportBristol University’s study on unconscious bias SF Haines’ post (Lecturer in Machine Learning at Bath University) –