Subscribe!

• Colins Blog

• How Not To Do Twitter
• Calculating 52 Factorial By Hand
• Small Things Might Not Be So Small
• Not If You Hurry
• Factoring Via Graph Three Colouring
• Another Proof Of The Doodle Theorem
• When Obvious Is Not Obvious
• Graph Three Colouring
• The Doodle Theorem
• Be Careful What You Say
• The Mutilated Chessboard Revisited
• A Mirror Copied
• The Other Other Rope Around The Earth
• Photocopy A Mirror
• The Point Of The Banach Tarski Theorem
• Sieve Of Eratosthenes In Python
• Fast Perrin Test
• Russian Peasant Multiplication
• FindingPerrinPseudoPrimes Part2
• FindingPerrinPseudoPrimes Part1
• The Unwise Update
• Miles Per Gallon
• Tracking An Item On Hacker News
• Hacker News User Ages
• Poking The Dusty Corners
• There Is No Time For This
• Publically Sharing Links
• Learning Times Tables
• Graceful Degradation
• Diagramming Maths Topics
• On The Rack
• Square Root By Long Division
• Beyond The Boundary
• Fill In The Gaps
• Software Checklist
• NASA Space Crews
• The Birthday Paradox
• The Trapezium Conundrum
• Revisiting The Ant
• The Ant And The Rubber Band
• Irrationals Exist
• Multiple Choice Probability Puzzle
• Random Eratosthenes
• Wrapping Up Square Dissection
• Dissecting A Square Part 2
• Dissecting A Circle
• Dissecting A Square
• An Oddity In Tennis
• Decision Tree For Tennis
• Decision Trees In Games
• A Matter Of Convention
• Do You Nourish Or Tarnish
• Binary Search Reconsidered
• Two Equals Four
• The Lost Property Office
• The Forgiving User Interface
• Setting Up RSS
• Withdrawing From Hacker News

• Random Writings.
• Colins Blog 2010
• Colins Blog 2009
• Colins Blog 2008
• Colins Blog 2007
• Colins Blog Before 2007

2016/05/31 ...

So the (modified) puzzle is:

When presented with that question, as phrased there, there are two initial reactions. One is to say that it's impossible, because a prime can never be a product. But the other is to start asking for clarification.

• Do you mean whole numbers?
  • ... and that's a whole 'nother kettle of fish ...
    • ... what exactly is a "whole number"?

• Is 1 a prime?

• Can I use negative numbers?

Until recently when I've been giving puzzles I've always answered those questions, but the responses from @DrBreitmaul brought me up short. He didn't solve the puzzle as I expected it to be. Well, actually he did, but he went much further.

You see, he asked each of those questions, and then proceeded to solve the puzzle for each of the possible answers. Instead of just taking one branch in the tree of possibilities, he investigated all of them. And the results were fascinating.

So here is a puzzle:

Now, ask a clarifying question:

The version Adam originally gave me, and the version I tweeted, explicitly says: Find three integers in arithmetic progression whose product is a prime. Stating it like that side-steps one of the possible explorations, whereas changing to a slightly less well-defined version opens more paths to explore. Including "What is a number?"

Suppose the answer is no, I wasn't intending to restrict you to whole numbers. Can you solve it then? How many different solutions can you find? Is there a structure to all of the solutions? How do you know you've found them all?

Then suppose the answer is yes, you are restricted to whole numbers. Now are there any solutions? How many different solutions can you find? Is there a structure to all of the solutions? How do you know you've found them all?

And so on. So there's a whole new meta-puzzle:

Go ...

<<<< Prev <<<< How Not To Do Twitter

:

>>>> Next >>>> Pythagoras By Incircle ...

---

You should follow me on twitter

Send us a comment ...