Unit 4 · Networks & Decision Mathematics · Escape Room
Sparky's just landed a massive electrical contract, but the apprentice (that's you) needs to solve 6 maths challenges before the job can go ahead. No shortcuts. Grab your calculator and your thinking cap. 🔧
Workshop Progress
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Challenge 1 of 6, Wire the Workshop
⚡ Challenge 1, Wire the Workshop
The workshop has 5 rooms (W, X, Y, Z, V) that all need connecting with electrical cable. Sparky wants to use as little cable as possible while still reaching every room. Use Kruskal's algorithm, sort the possible connections from shortest to longest, then keep adding cable unless it creates a loop.
🔌 Task, Minimum Spanning Tree
💡 Method: Sort edges → add shortest that doesn't create a cycle → stop at n − 1 edges
What is the minimum total cable length (in metres) needed to connect all 5 rooms?
🗺️ Challenge 2, Plan the Installation
Sparky's got 5 tasks to complete the switchboard upgrade. Some tasks can only start once others are done. Use the forward pass (take the MAX at joins) to find the earliest each task can start, then find the minimum total time for the whole job.
⏱️ Task, Critical Path (EST / Forward Pass)
💡 EST = maximum of (EST + duration) of all predecessor activities
Task
Description
Duration (hrs)
After
A
Test power supply
2
,
B
Run conduit
4
A
C
Pull cables
3
A
D
Connect circuits
5
B, C
E
Install safety switches
2
D
What is the minimum number of hours to complete the full installation?
⏱️ Challenge 3, Slack Time
Good news, Task C (Pull cables) has some wiggle room! Use the backward pass (take the MIN at forks) to find each Latest Start Time, then calculate the float. Float = LST − EST. Float = 0 means it's critical. Float > 0 means it can be delayed without affecting the finish.
🔍 Task, Float Time (same network as Challenge 2)
💡 LST(D) = finish time − duration of D. LST(C) = LST(D) − duration of C. Float(C) = LST(C) − EST(C)
Task
Duration
EST (from ←)
LST (to find →)
A
2
0
0
B
4
2
2
C
3
2
?
D
5
6
6
E
2
11
11
How many hours of float does Task C (Pull cables) have?
👷 Challenge 4, Assign the Crew
Sparky has 3 apprentices (Ash, Blake, Cruz) and 3 jobs to assign. Each person takes a different number of hours on each job. Use the Hungarian algorithm, row reduce, column reduce, then find the optimal one-to-one assignment, to minimise total labour hours.
🏆 Task, Hungarian Algorithm (3 × 3)
💡 Row reduce (subtract row min) → Column reduce (subtract col min) → Assign zeros (one per row, one per column)
Apprentice
Rewire Kitchen
Lay Conduit
Wire Circuits
Ash
5
3
8
Blake
2
7
4
Cruz
6
4
5
Numbers = estimated hours. Each apprentice gets exactly one job. Find the assignment that gives the lowest possible total hours.
What is the minimum total labour hours?
🌏 Challenge 5, International Call
Sparky's scored an international electrical contract! A client in Singapore (UTC+8) needs to schedule a video call. It's currently 2:00 PM (1400) in Brisbane (AEST, UTC+10). Singapore is 2 hours behind Brisbane, so you need to subtract 2 hours.
What time is it in Singapore? Give your answer as a 4-digit 24-hour time (e.g. 0900 for 9:00 AM).
💰 Challenge 6, Final Invoice
Last challenge! The Singapore job is booked and it's time to send the invoice. Sparky charges a $150 call-out fee, then $85 per hour. The job takes exactly 6 hours. Calculate the total invoice amount, get this right and you've earned your certificate! 🎉