The Unknown Puzzle

This week’s puzzle comes from my Science Times colleague Ben Carey, who tells me that you really don’t have to be smarter than a fifth-grader to solve it. I don’t take much consolation from his assurance, given that the puzzle utterly stumped me, but I respect Ben’s authority on the subject of fifth-graders and puzzles. He’s the author of “The Unknowns,” a novel for young adults, in which the pre-teen inhabitants of a trailer park have to solve a series of math puzzles in order to navigate a tunnel network and save their community from catastrophe.

My son, who’s in fourth grade, loved the novel and managed to pick the correct answer to this puzzle, but he confessed that he was guided by intuition and wasn’t able to give a logical explanation for his choice. (Maybe he’d have gotten it in fifth grade.) To be eligible for the solvers’ prize — a copy of “The “Unknowns” — you have to give a reason for the answer you choose below:

The Unknown PuzzleAmulet Books Consider the four shapes in the top row followed by a blank space in the fifth position. Which of the possibilities in the bottom row — the shapes labeled A, B, C, and D — would most logically belong in that fifth position?

As usual, you can post your answer as a comment here, and submit another puzzle either as a comment or by emailing tierneylab@nytimes.com. (Please email me a solution to the puzzle and indicate whether or not it’s original.) I’ll award the prize to someone who comes up with an especially interesting answer or to someone who proposes a sufficiently intriguing puzzle for Lab readers to solve. The Lab judges may look kindly on answers given in verse, perhaps ones that delve into the theme of things unknown. Although we expect it will be difficult for anyone to supersede the philosophical musings on this subject by Donald Rumsfeld when he was secretary of defense:

. . . there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns — the ones we don’t know we don’t know.”

There is actually some logic to what he said — and to those shapes in this week’s puzzle. Hope you have better luck than I did.

And if you haven’t yet tried last Monday’s Russell Crowe Hotel Puzzle, today’s the last chance to try for the prize. Tomorrow we’ll announce the prize and discuss ways to find Mr. Crowe a room at the Hotel Infinity.

Comments are no longer being accepted.

A is the right answer. You have a series of odd numbers in your shapes so either A or B is the answer, but none of the previous shapes have parts of the numbers crossing over the vertical divide, as choice B does. It’s a mirror type of picture.

~20 years old

Spinning as I do this. April 27, 2009 · 11:00 am

The answer is B.

All four are artsy views of a bicycle and some of its parts, and B is the rider of that bike.

The answer is B.

The shapes are the numbers 1, 3, 5, & 7 with their mirror image.

A, which is created by starting with the number 9, then placing a vertical mirror on the number’s left side and adding the reflection. The four shapes leading up to the blank are similarly the numbers 1, 3, 5 and 7 and their reflections, which is a simple sequence of odd numbers. It’s not B, because the 9 in B isn’t reflected in the same way (there’s a wrong overlap). It’s not C, because it’s not a 9 and its reflection. And it’s not D, because the font doesn’t match, and because there’s probably a bit of overlap as well.

My answer is B — I don’t know why but that’s what my intuition is telling me. I will email you a puzzle.

Answer is A. Mirror image and image of the numbers 1,3,5,7 etc. Next in sequence is 9.

I would have to guess that the answer is A.

I think the series, if I am right, is the odd numbers in reflection. I.e. 1, 3, 5, 7 with their mirror images. This would make 9 the next one in the sequence. Reminds me of a test performed by a psychologist some years ago where you write the letters of the alphabet above and below a line. Kindergartners were significantly more likely to guess where the next letter fell vs. college graduates. The beginning of the sequence is below:

A EF HI

BCD G J

Where would I place K?

…it took me about 3 minutes…these figures are numbers with a mirror image on the left side (is that clear?)…the first number is 1, followed by 3, followed by 5, followed by 7, and the last number is 9…which is A…

A: The images are composed of the odd numbers 1,3,5,7,9,… joined together with their mirror images (mirrored across a vertical line). The next one after what’s above would be something like two copies of the first image.

Sorry just realized the answer is actually A.

Answered too quickly, the mirror line is at the left edge of each number not the center point.

Shape #3 incorporates the bottom half of shape #2. If you generalize this property to all odd-numbered shapes, you can expect #5 to incorporate the bottom half of shape #4.

This leads to choice A.

…so, how did i solve it? Well, after looking at it for a minute…I did my Wheel of Fortune problem solving…is it A, B, C, D ? No…is it 1, 2, 3, 4….No….then I went back to the first symbol and the Number 1 jumped out at me….but, wait, the second symbol looks like an 8…that is not correct…then I realized the 8 could be a 3 doubled over…and then it was Eureka !!! I looked for a “5” in the third symbol…and there it was staring me in the face…I picked the Answer while typing my solution…a fun puzzle indeed !!!

1, 3, 5, 7… 9!

so A is the next.

The images are what you would see if you held numerals up next to a mirror so you could see the original and the reflection merged into a single shape.

Each shape is composed of an odd number and its mirror image. Imagine writing each of the numbers 1, 3, 5, and 7 on a piece of paper, and (for each in turn) positioning a vertical, right-facing mirror at the leftmost edge of each digit. Looking into the mirror, you’ll see the above shapes spanning the mirror and the paper. The next shape in the sequence therefore corresponds to the number 9, as given by A.

A; the first four are 1, 3, 5, and 7 forward and backward next to each other. Choice A follows the pattern by being 9 in the same format.

A – to complete the sequence of odd numbers and their reflection… wasn’t a very similar puzzle on the Simpsons, Lisa couldn’t solve it and it made her question her own intelligence?

The answer is A. Each figure is the mirror image of an odd number with the mirror line positioned in the left side of the number. The sequence goes , in the sequence 1, 3, 5, 7… so the next figure is logically the number 9, mirrored on its left side.

The answer I am glad to say,
Is the figure by letter A.
To those unsure, it may be clearer,
If you get yourself a mirror.
Place it next to digits odd,
Take a look – you will surely nod.
For you will now plainly see
The neither B, C, or D,
Fits in to the fifth position.
As is clear in this exposition:
Each figure is an odd number’s reverse,
Joined to itself, for better or worse.
With 1, 3, 5, and 7 provided,
To the number 9, we are guided.
And so that gives us option A,
And we’re done – hip, hip, hooray!

I think the answer is A.

It looks like the numbers are 1, 3, 5, 7, each joined with its mirror image. A) continues the pattern with 9.

The answer is A. The shapes are odd numbers (1,3,5,7) with vertical symmetry. The left half of the shape is the number reversed. Thus, 9, inverted on the left and vertically symmetric on the right, is the next shape in the sequence.

I think I remember this one from the fifth grade, actually. Place a small mirror on a vertical line in the middle of each of the symbols, and it becomes clear. It’s A, which is the number nine and its mirror image, the series being 1,3, 5, and 7, all with the same representation.

The only answer I can justify is A.

The pattern I see is that the following symbol shares a visual similarity with the top or bottom half of the symbol that precedes it. The other half of the element changes unpredictably. The half that stays similar alternates every element.

So, in the second and third elements of the sequence, the bottom half of the symbol stays the same (ie an oval) and the top portion of the symbol changes from a curved shape to a flat line. Element 4 preserves the top element of symbol three (a flat line) and adds a new bottom portion (the pointy triangle bottom). Element A follows element 4 because it retains the bottom portion of figure four while adding a new type of top element (two circles instead of a straight line).

The first element doesn’t perfectly fit into my framework, although the top of the figure does share some visual similarity with the top element of figure two as my pattern says it should.

The answer is A.

Each of the items in the series is an odd number that has been placed next to a mirror image of itself.
The first is the number 1, then 3, then 5, then 7.
The answer is A because it is a 9 that has been placed next to its mirror image.

This is very similar to a puzzle from the Simpsons that stumped Lisa and convinced her that she would lose her intelligence. It is more clear if you write each symbol below the previous one and then cover up the left side (which is simply a mirror image of the right). In the Simpsons the numbers were in sequential order but in this puzzle it is a series of odd numbers. So A is correct (1,3,5,7,9)

The answer is A.

Each symbol is an odd number on the right coupled with its mirror on the left. The sequence simply goes “1”, “3”, “5”, and “7” . So, the fifth symbol should be a mirrored “9”, mirrored in the particular way option A is.

It’s important to note that number and its mirror don’t overlap except on the mirrored axis in the sequence; otherwise, B might be a tempting answer. Also, the exact style of the numbers is relevant; the numerals are mirrored using standard curvy script, excluding D because of its alarm clock-esque blockiness – even though it follows the technical requirements of the mirroring symbology.