A Conway Puzzle Solution (And Some Hints for the Other Puzzle)

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Two weeks ago, in honor of mathematician and puzzly spirit John Horton Conway, we shared two of his favorite brain teasers and challenged our fellow PuzzleNationers.

So today, we happily share the solution for puzzle #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?

Both windows are perfect squares, 1 meter wide and 1 meter high. So how can there be a difference in the amount of light?

The trick of this puzzle is in the description. Although the original window was a perfect square, the dimensions of the square aren’t 1 meter by 1 meter. No, it was a square placed like a diamond, with one corner directly above its opposite. So the 1 meter dimensions were the diagonals, not the sides.

All the Miracle Builders had to do was build a square window in the usual arrangement (two sides horizontal, two sides vertical) with dimensions of 1 meter by 1 meter. That creates a larger window (with a diagonal of √2m) and allows more light.

Very tricky indeed.


We had several solvers who successfully cracked the Miracle Builders puzzle, but there was less success with puzzle #2, The Ten Divisibilities.

So, in addition to the original puzzle, we’re going to post some solving hints for those intrepid solvers who want another crack at the puzzle.

The Ten Divisibilities

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

  • 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…]

Here’s a few hints that should help whittle down the possibilities for any frustrated solvers:

-If you add all the digits in a number, and the total is divisible by 3, then that number is also divisible by 3.
-If the last two digits of a number are divisible by 4, then that number is divisible by 4.
-If the last three digits of a number are divisible by 8, then that number is divisible by 8.

Good luck, and happy puzzling!


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Intuitive vs. Non-Intuitive Puzzles

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[Image courtesy of The Spruce Crafts.]

Sometimes, when you look at a puzzle, you know immediately what to do and how to solve. In my opinion, a great deal of Sudoku’s success is due to its intuitive nature. You see the grid, the numbers, and you know how to proceed.

Crosswords are similarly straightforward, with numbered clues and grid squares to guide new solvers. (The “across” and “down” directions also help immensely.)

That’s not to say that these puzzles can’t be off-putting to new solvers, despite their intuitive nature. I know plenty of people who are put off by crosswords simply by reputation, while others avoid Sudoku because they’re accustomed to avoiding ANY puzzle that involves numbers, assuming that some math is involved. (I suspect that KenKen, despite its successes, failed to replicate the wild popularity of Sudoku for similar reasons.)

But plenty of other puzzles require some explanation before you can dive in. A Marching Bands or Rows Garden puzzle, for instance, isn’t immediately obvious, even if the puzzle makes plenty of sense once you’ve read the instructions or solved one yourself.

The lion’s share of pen-and-paper puzzles fall into this category. No matter how eye-catching the grid or familiar the solving style, a solver can’t simply leap right into solving.

Thankfully, this won’t deter most solvers, who gleefully accept new challenges as they come, so long as they are fair and make sense after a minute or so of thought. Cryptic crossword-style cluing is a terrific example of this. At first glance, the clues might appear to be gibberish. But within each clue lurks the necessary tools to unlock it and find the answer word.

Brain teasers often function the same way. You’re presented with a problem — a light bulb you can’t see and three possible switches for it, for instance — and you need to figure out a way to solve it. It might involve deduction, wordplay, or some clever outside-the-box thinking, but once you find the answer, it rarely feels unfair or unreasonable.

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[Image courtesy of Deposit Photos.]

But, then again, there are also puzzles that can baffle you even once you’ve read the instructions and stared at the layout for a few minutes. Either the rules are complex or the solving style so unfamiliar or alien that the solver simply can’t find a way in.

In short, puzzles as a whole operate on a spectrum that spans from intuitive to non-intuitive.

Want an example of baffling or non-intuitive? You got it.

GAMES Magazine once ran a puzzle entitled “Escape from the Dungeon,” where the solver had to locate a weapon in a D&D-style dungeon. A very small crossword puzzle was found in one room on a paper scroll.

But the solution had nothing to do with solving the crossword.

The actual solution was to take the crossword to a magician who removed letters from the fronts of words. Removing the C-R-O-S left you with a sword, completing the overall puzzle.

That sort of thinking is so outside the box that it might as well be in a different store entirely. Video games, particularly ones from the point-and-click era, have more than their fair share of non-intuitive puzzles like this. You can check out these lists for numerous examples.

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And as escape rooms grow in popularity, more of them seem to be succumbing to less intuitive puzzling as a result of trying to challenge solvers.

For example, in one escape room I tried, various fellow participants uncovered two stars, a picture of the three blind mice, and four different items that represented the seasons. Amidst all the locks to open, puzzles to unravel, and secrets to find, it never occurred to any of us that these three unconnected numbers would have to be assembled as a combination to a lock. By asking for a hint, we were able to figure out to put them together and open the lock, but it’s not a terribly intuitive puzzle.

Perhaps the greatest challenge for a puzzle constructor — be it a pen-and-paper puzzle, an escape room scenario, or a puzzle hunt dilemma — is not creating a dynamite, unique puzzle, but ensuring that finding the solution is fair, even if it’s difficult or mind-boggling.

This sort of thinking informs not only my work as a puzzlesmith, but the designs for my roleplaying games as well. If my players encounter a gap, there’s some way across. If there’s a locked door, there’s a way through it. Oftentimes, there’s more than one, because my players frequently come up with a solution that eluded me.

In the end, that’s the point. All puzzles, no matter how difficult, exist for one reason: to be solved. To provide that rush, that a-ha moment, that satisfaction that comes with overcoming the clever, devious creation of another sharp mind.

And non-intuitive puzzles are tantamount to rigging the game.


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Answers to Our Thanksgiving Logic Puzzle

We’re halfway to Christmas already, but remember Thanksgiving? It wasn’t all that long ago, we swear!

We celebrated the holiday by posting a fun little logic puzzle for our fellow puzzlers and PuzzleNationers. And we’re overdue to post the solution to our little dinner dilemma!

So, without further ado, let’s get to work!


Four girls — Emma, Taylor, Madison, and Morgan — are waiting for the Thanksgiving dinner.

Each is a different age (8, 9, 10, or 11) and looking forward to eating a different Thanksgiving staple (turkey, mashed potatoes, stuffing, or pumpkin pie).

Can you puzzle out the age and favorite Thanksgiving food of each girl from the clues below?

  • Madison is looking forward to eating turkey.
  • The girl who likes pumpkin pie is one year younger than Morgan.
  • Emma is younger than the girl that loves turkey.
  • The girl who likes stuffing is two years older than Morgan.

So where do we start? Simple. We start with Morgan.

Why Morgan? Because we have two clues connected to her that mention ages, clues 2 and 4.

There is a girl one year younger than Morgan and a girl two years older. Since the ages are 8, 9, 10, and 11, that means Morgan must be 9 years old.

thankspuzzle1

Now let’s look at clue 3. The girl who loves turkey is either age 9 or 10, since we already have foods for the other ages. Emma is younger than that girl. The only way Emma can be younger than age 9 or 10 is to be 8 years old.

So let’s fill that part in.

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Sticking with turkey-related clues, we can now look at clue 1. If Madison is the one who likes turkey, she has to be age 10, because that’s the only age in the chart with both the girl’s name and the favorite food uncompleted.

And by process of elimination, that means Morgan likes mashed potatoes and Taylor likes stuffing.

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How did you do, fellow puzzlers? Did you solve the logic puzzle in time for turkey dinner? Let us know in the comments section below! We’d love to hear from you.


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Answers to the Punderful Halloween Costume Game!

Halloween has come and gone, but the glorious puns remain.

That’s right, today we’ve got the answers to our latest edition of the Punderful Halloween Costume Game!

So, without further ado, let’s take a look at the punny answers!


#1

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It’s Hawaiian Punch!

[Image courtesy of Hikendip.]

#2

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It’s back to the drawing board for this fella!

[Image courtesy of Country Living.]

#3

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It’s Scar-Face!

[Image courtesy of Upbeat News.]

#4

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It’s prime rib!

[Image courtesy of The Kitchn.]

#5

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It’s a Rey of sunshine!

[Image courtesy of Hannah Sloan.]

#6

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Snitches get stitches in this lovely mix of idiom and Harry Potter!

[Image courtesy of sprace.]

#7

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It’s a two-fer here with the cat’s pajamas and the bee’s knees!

[Image courtesy of Devon Prokopek.]

#8

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It’s a creative outlet!

[Image courtesy of Mental Floss.]

#9

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It’s chicken cord on blue (chicken cordon bleu)!

[Image courtesy of Hikendip.]

#10

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It’s Edgar Allan Poe Dameron in this mix of Star Wars and classic literature!

[Image courtesy of rottenartist.]


How many did you get? Have you seen any great punny costumes we missed? Let us know!

Thanks for visiting PuzzleNation Blog today! Be sure to sign up for our newsletter to stay up-to-date on everything PuzzleNation!

You can also share your pictures with us on Instagram, friend us on Facebook, check us out on TwitterPinterest, and Tumblr, and explore the always-expanding library of PuzzleNation apps and games on our website!