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!

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).

Challenge #3 – The Devil’s Tail – Solution

This is the solution to Challenge #3 – The Devil’s Tail, make sure you check that post out before looking at the solution!

This Challenge is a modification of a famous problem which confused many people – The Boy-Girl paradox.

So, it turns out that “Heads” is the most probable at 67%. But why?

The devil could have any of the 3 combinations: {HT, TH, TT}, and 2 of those include a Heads! A common answer is “Equally Likely” as it is easy to assume that the devil showed us a specific coin, meaning the remaining coin is equally likely to be Heads or Tails, but this is not the case as we do not know which coin the devil showed us. Some people’s intuition may also have lead them to think it might be Tails as we have already had a Tails, but this is also not true. Hopefully this problem illustrates how probability is very deceptive and counter-intuitive!

Challenge #2 – The Elements – Solution

This is the solution to Challenge #2 – The Elements, make sure you check out the challenge before looking at the solution!

Trust the devil. Why?

The first clue given in the challenge is the note left behind by Doctor Aro.

The key piece of information on the note says that we have to reflect on the odd things in life.

Reflecting the position of the digits in the odd numbers we get:
71 6 53 9 68
(Reflecting the position of the digits for 9 leaves it the same)

But how do we decipher the numbers?

Dr Aro was ‘dabbling in the chemical arts’ and this challenge is called ‘The Elements’, written in a similar way to the elements in the periodic table.

Using the periodic table we get:

Lucifer i.e. the devil 😈

Were you able to save Doctor Aro?

Challenge #1 – Prison Break – Solution

This is the solution to Challenge #1 – Prison Break – make sure you check that post out if you haven’t already!

It turns out that Guard C is your friend!

We are given the information that each robot guard always lies for the whole day, or always tells the truth for the whole day. This information does not indicate that the guards have truth/lie days in any particular order.The robot guards could have truth/lie days as follows: Truth, Lie, Truth, Lie, …
But equally could have days as below:
Truth, Truth, Truth, Lie, …

There is no reason to presume that the guards all follow the same orders, so we can assume that each guard is independent of the others. This means a guard’s truth/lie days can be different to the other guards.

So why is Guard C our friend? Guard C said “Today, I lie.”

  • If Guard C is telling the truth, then it means Guard C is lying as indicated from the statement.
  • – If Guard C is lying, then Guard C has just told us the truth about lying.

Guard C’s statement is a paradox!

Paradoxes like the one presented in this challenge, also known as “Liar’s paradox”, are attributed to the ancient Greek seer Epimenides (fl. c. 6th century BCE). Epimenides, an inhabitant of Crete, famously declared that “All Cretans are liars”.

This paradox will arise whenever the statement refers to whoever is claiming the lie themself.

Consider: “This sentence is a lie”.

This circular logic is important in part because it creates severe difficulties for logically rigorous theories of truth; it was not adequately addressed (which is not to say solved) until the 20th century.