First, the bad news. There’s a werewolf on the loose.
But don’t worry, there’s good news: You’ve narrowed the werewolf down to four suspects and you’ve taken a hair sample from each.
Alas, more bad news: your clumsy lab assistant has mixed up the hair samples. Each bag now contains hair from multiple suspects, hopelessly mingled together. If a bag tests positive, you’ll know one of those suspects is the werewolf, but not which one it is.
Further bad news: your assistant can only find two testing kits. It’s 11pm, and the tests take 50 minutes to develop, so you’ve got to choose two bags to test right now.
How can you use two tests to identify the werewolf before midnight?
***
Now, you may not believe it, but that werewolf business was a work of fiction. That’s right: the vivid details, the photorealistic illustrations, the highly plausible names… all deceptions. In truth, there is no werewolf, no clumsy assistant, and (unless you know something I don’t) no bags of hair. Rather, this scenario comes—and here’s the best news of all—from a new book I’ve been working on.
Ladies and gentlemen, assistants and werewolves: welcome to Puzzle Planet.
I am ludicrously excited about this one. I’ve spent two years gathering puzzles, polishing puzzles, theorizing about the nature of puzzles, and foisting puzzles upon friends, strangers, and unsuspecting spouses. (I find that after enough puzzle-foisting, unsuspecting spouses eventually become suspecting ones.)
Now, it is my sincere hope to foist these puzzles upon you. If you’re interested, you can sign up here to help me play-test material for this upcoming book.
You have questions, have you? Then I have answers, have I!
What kinds of puzzles?
Here are the ways I’ve described them in recent months to strangers (most of them friendly) and to friends (most of them strange):
- “Playable”
- “Game-like”
- “Mathy”
- “Not, like, school-mathy”
- “Hands-on”
- “Dive-in-to-able”
- “Accessible to middle schoolers”
- “Requiring nonzero thought from math professors”
- “Intended to give you—if only briefly—the maddening joy of being stuck”
Who do you want as play-testers?
Anyone willing! But I’m especially eager to recruit: (1) young’uns from ages seven to seventeen, (2) math teachers who want to try the puzzles with their classes, and (3) other puzzle fans of the sort who might buy the eventual book.
How will the playtesting work?
- You fill out a form letting me know you’re interested.
- I email you a PDF with puzzles to enjoy at your leisure.
- You give feedback via a Google Form.
- Your collective generosity and wisdom help me to clarify confusing bits, fine-tune difficulty levels, cull inferior puzzles, spotlight superior ones, and sprinkle play-testers’ insight and wit throughout the text. The final book glows with your contributions. Puzzle-love sweeps the world. Earth enters a new golden age. Cities smell of rose and cardamom. Human and dog develop a mutually intelligible language and pen joint works of philosophy. That sort of thing. All thanks to you.
When can I expect these puzzles?
Starting later this month. They’ll come in batches; I want to stagger play-testing so I can incorporate feedback and iterate my way to the best version of each puzzle.
What’s the answer to that werewolf one?
Have you tried it already?
Um… no.
Then no spoilers!
Okay, I’ve tried it now. What’s the answer?
So, when you test two bags, there are four possible outcomes: (1) both positive, (2) both negative, (3) only the first is positive, and (4) only the second is positive.
We need each of those outcomes to signify a different suspect. Which means we need our suspects’ hair to appear, respectively, (1) in both bags, (2) in neither bag, (3) only in the first bag, and (4) only in the second bag.
One solution: test AD and BD. The other solution, equally valid: test BC and BD.
Cool. Can I have another sample puzzle?
Sure! That’s what I’ve been saying! Just sign up here…
Math with Bad Drawings 
Always absolutely love your sense of humor and great mathematical lessons! Keep up the great work ! 🙂 Jeanne Lazzarini
So exciting! My grandson and I loved testing for your Math Games with Bad Drawings book. I’ve already forwarded this to HIM and to a few elementary school math teachers I volunteer for (those kids LOVE puzzles, I give them puzzles every week). Should be a GREAT book.
What I love about the werewolf puzzle is how cleanly it rewards a change in viewpoint: at first it feels like a story problem about bags of hair, but the real move is to realize you are designing four distinct outcome-signatures from two yes/no tests. The jump from “which bags should I test?” to “I need one suspect in both bags, one in neither, one only in the first, and one only in the second” is exactly the kind of elegant restructuring that makes a puzzle memorable. Choosing AD and BD is satisfying not because it is complicated, but because it makes the whole space of possibilities snap into focus at once. That is a rare puzzle virtue: the solution feels both surprising and inevitable. If this example is representative of Puzzle Planet, then the book is aiming at something much better than routine cleverness—it is aiming at puzzles that teach you how to think without ever sounding like they are teaching.
So true! Insightful.
I have no email. But I like the 75.25 games. It inspired me to create new games.
（under 25 years old）