Algebra + Train Track Sudoku = Algetrainoku
Difficulty Level: Grade 10 Algebra & Spatial Logic (Accessible to anyone with basic high school algebra skills!)
Hello Reader!
My name is Olivia, and I’m a Toronto-based piano teacher and tutor. I hated math in high school, but back in 2024, I had the opportunity to teach high school math and chemistry—and that’s where I finally found an appreciation for it.
It’s a weird story, so let me tell you about it! I teach three boys whose mother is the head of the math department at a high school up north in Georgina, Ontario. She let me know that they desperately needed a supply teacher because they were three weeks into the new school year and several classes had no one to supervise the kids. I don’t hold formal teaching credentials, but the school board made an exception and allowed me to come in as an emergency supply while they searched for a permanent teacher.
I opened the Grade 11 Functions textbook and realized, I can easily teach this! I relearned the first chapter and taught it to the class—I figure I might as well get them started on something rather than let them spend the semester missing core units. I created games and quests for my students, including a dragon egg hunt for my Grade 9s (where completing a series of worksheets earned them a chance to win a dragon egg that granted an extra point on a test). A week passed, no permanent teacher had been found, and I had built great connections with my students. A group of them actually went to the principal to ask if I could stay as their permanent teacher—and the school board signed off on it! That experience unlocked a love for high school math I never knew I had.
Fast forward to 2026, and here we are! I’m creating educational resources, running my student mail club (check it out at www.olivialim.ca if you have a child in Kindergarten to Grade 5!), and designing logic puzzles. Here’s my very first one! The first person to solve it wins a picture of one of my cats!
(If you have a pocket notebook but have no clue what to write in it, these Algetrainoku puzzles are perfect for it!)
The Case of the Junction Express
An express train hurtles through the midnight fog along a remote, four-station stretch of timber country: Alpha, Beta, Gamma, and Delta. A coded dispatch was intercepted at the yardhouse, but the route map has been sabotaged. You must decipher the conductor's ledger at each junction to reveal the track constraints. One mistake in your calculations, and the Express plummets off a ghost spur.
Act I: The Fog at Alpha Junction
A solitary lantern swings on the deserted platform of Alpha Station as the clock tower strikes 8:00 AM. Engine 99 roars out of the yard, accelerating into a dense fog toward Beta Station over an unmapped expanse of x kilometers. The speed gauge locks at a continuous (x + 20) km/h, and the locomotive tears through the shadows for exactly 45 minutes (0.75 hours) before its brakes screech to a halt in the Beta freight yard. How far into the dark did the train travel? (Clue: Distance = Speed x Time)
Act II: The Secret Ledger at Beta
In the shadows of Beta Station, a crowd boards. The passenger count, y, is 40 fewer than the distance x from Alpha. Standard tickets cost $12.00, while mysterious travellers in the parlour car carry Premium (P) tickets worth $20. The conductor’s ledger shows exactly $360 collected. How many Premium passengers, P, crossed the threshold? (Clue: Standard Passengers = y - P)
Act III: The Midnight Works at Gamma
Farther down the line toward Gamma Station, steam rises from an ironworks forge where night crews are hurriedly finishing a critical bridge expansion. The blueprint specifies a total amount of z track segments, governed by the formula 3P + 35. Heavy timber Straights (S) cost $500 each, while reinforced Curved (C) iron rails cost $800 each. A ledger left on a workbench shows the foreman exhausted the entire secret budget of $43,000. How many Curved iron rails, C, were bolted down? (Clue: S + C = z)
Act IV: The Sabotaged Labyrinth at Delta
The Express slows to a crawl at the approach to Delta Station. Ahead lies a dark 6 times 6 switching yard where the tracks have been scrambled by an unknown operative. To unlock the safe route, calculate the yardmaster’s key, k, which equals the number of curved rails C minus 8. The train enters at the Top of Column 1 and must escape through the Right side of Row 4. A cryptic message carved into the signal box dictates the exact segment capacities for the grid:
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