Two Brain Teasers, Courtesy of Conway


Last week, we penned a post celebrating the life and puzzly legacy of mathematician John Horton Conway, and several of our fellow PuzzleNationers reached out with their own thoughts or questions about Conway.

One recurring subject was about his love of puzzles and what kind of puzzles he enjoyed solving. So, naturally, I went hunting for some of Conway’s favorite puzzles.

As it turns out, Alex Bellos of The Guardian had me covered. Alex has a recurring puzzle feature on The Guardian‘s website where brain teasers and other mental trickery awaits intrepid solvers.

Years ago, Alex had asked Conway for suggestions for his column, and Conway offered up two tricky puzzles.

And now, I happily share them with you.

#1: The Miracle Builders

I had a window in the north wall of my house. It was a perfect square, 1 meter wide and 1 meter high. But this window never let in enough light. So I hired this firm, the Miracle Builders, who performed the impossible. They remodeled the window so it let in more light. When when they’d finished the window was a perfect square, 1 meter high and 1 meter wide.

How did they do it?

#2: The Ten Divisibilities

I have a ten digit number, abcdefghij. Each of the digits is different.

The following is also true:

  • a is divisible by 1
  • ab is divisible by 2
  • abc is divisible by 3
  • abcd is divisible by 4
  • abcde is divisible by 5
  • abcdef is divisible by 6
  • abcdefg is divisible by 7
  • abcdefgh is divisible by 8
  • abcdefghi is divisible by 9
  • abcdefghij is divisible by 10

What’s my number?

[To clarify: a, b, c, d, e, f, g, h, i, and j are all single digits. Each digit from 0 to 9 is represented by exactly one letter. The number abcdefghij is a ten-digit number whose first digit is a, second digit is b, and so on. It does not mean that you multiply a x b x c x…]

Did you solve one or both of these fiendish mind ticklers? Let us know in the comments section below! We’d love to hear from you.

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3 thoughts on “Two Brain Teasers, Courtesy of Conway

  1. Pingback: A Conway Puzzle Solution (And Some Hints for the Other Puzzle) | Blog

  2. Pingback: Answer to the Fiendish Second Conway Puzzle, The Ten Divisibilities! | Blog

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