Two options on the board — “as a bicycle courier, would you rather be paid 60 cents per kilometre ridden, or a flat 18 dollars per hour?” — and one rule: your preference is worthless until mathematics backs it. Most good prompts hide a third answer behind the two printed ones: it depends — and the game is finding on what.
How we play
- Choose a side in silence. Commit before calculating feels safe.
- Defend with numbers, a table, or a sketch — not with vibes.
- Hunt the tipping point: where, exactly, does the better choice switch?
The courier duel, argued
- “The flat rate, obviously — you get paid even at red lights.”
- “Convert them to the same units first. At a riding speed of kilometres per hour, the per-kilometre deal pays dollars per hour. Now the two offers can actually fight.”
- “Tipping point: gives . Below 30 km/h, take the flat rate; above it, take the distance rate.”
- “So it depends on your average speed across a shift — gridlock afternoons and open-road mornings crown different winners. And notice what the comparison secretly required: turning a rate per kilometre into a rate per hour meant multiplying by a rate of kilometres per hour. Chaining rates together like that is not a trick, it is a law — the same one The Chain Rule states for functions.”
One variation
“Would you rather land in a plane with a small velocity at touchdown, or a small acceleration?” Velocity is how hard the wheels hit; acceleration is what your stomach feels on the way down — the rate of the rate. A descent can be slow and still lurching, or brisk and glass-smooth. Deciding which quantity comfort actually lives in is a warm-up for Smooth Landing, where your group must design a descent whose height, velocity, and acceleration all behave — and Motion on a Line gives the three quantities their exact relationship.
"It depends" is a mathematical answer
The strongest defence names the variable it depends on and the exact value where the choice flips. For the courier duel that variable is average speed and the flip is 30 km/h — and the difference between an average rate and the rate right now is where The Speed Camera raises the stakes to a ticket in court.