The 5 Machines Problem: Can You Outsmart the Scaling Trap?
⚙️ Machines and widgets puzzle
Maidin mhaith, quizzers! 👋 Welcome to part two of our mini-series (start with part one if you missed it), diving into three famous logic puzzles that challenge how we think — and how easily our brains can be tripped up by questions that seem straightforward.
These puzzles come from the Cognitive Reflection Test, used in psychological studies at universities like Princeton and MIT to examine how we balance intuitive vs reflective thinking. While the answers seem obvious at first glance, that first instinct is often wrong — and that’s what makes them so powerful.
Today’s puzzle is all about scale and speed. Can you figure out how long it takes 100 machines to make 100 widgets — without falling for the intuitive trap?
Question: If it takes five machines five minutes to make five widgets, how long would it take 100 machines to make 100 widgets?
Solving the widgets problem
Drumroll please… tap to reveal the explanation!
Step 1: Understand the rate of production
5 machines take 5 minutes to make 5 widgets.
So, 1 machine takes 5 minutes to make 1 widget — this is the unit rate.
Step 2: Scale up to 100 machines
Each machine still makes 1 widget in 5 minutes.
So, 100 machines working in parallel will each produce 1 widget in 5 minutes.
Step 3: Solve for total output
In 5 minutes, 100 machines produce 100 widgets.
Conclusion
100 machines take 5 minutes to make 100 widgets. ✅
If your first instinct was “100”, you’re not alone — this is the most frequent wrong guess. Many assume more widgets = more time, forgetting that more machines = faster output.
By now, you’ve tackled two of the most famous logic puzzles (start with part one), used in cognitive studies. You're building your reflective thinking muscles, and there’s one more challenge to go.
This Friday, we’ll explore a deceptively gentle riddle involving a lake and a patch of lily pads — but it’s secretly a lesson in exponential growth. Thanks for playing — agus slán go fóill!
Ready for more?
Join the conversation 💬
How did you get on? Got thoughts, scores, or reckon you’ve spotted something? Drop your comments below! ✍️
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