WODB, Quora Style

The following puzzle was recently posted on Quora:

Which of the following numbers don’t belong: 64, 16, 36, 32, 8, 4?

What I liked about this puzzle was the answer posted by Danny Mittal, a sophomore at the Thomas Jefferson High School for Science and Technology. Danny wrote:

64 doesn’t belong, as it’s the only one that can’t be represented by fewer than 7 binary bits.

36 doesn’t belong, as it’s the only one that isn’t a power of 2.

32 doesn’t belong, as it’s the only one whose number of factors has more than one prime factor.

16 doesn’t belong, as it’s the only one that can be written in the form x^y, where x is an integer and y is a number in the list.

8 doesn’t belong, as it’s the only one that doesn’t share a digit with any other number in the list.

4 doesn’t belong, as it’s the only one that’s a factor of all other numbers in the list.

I suspect that Danny has visited Which One Doesn’t Belong or has read Christopher Danielson’s Which One Doesn’t Belong. Or maybe he’s just a math teacher groupie and trolls MTBoS.

But then Jim Simpson pointed out the use of “don’t” in the problem statement, which I had assumed was a grammatical error. Jim interpreted this to mean that there must be two or more numbers that don’t belong for the same reason, and with that interpretation, Jim suggested the answer was 32 and 8, since all of the others are square numbers.

Don’t get me wrong — I don’t think this is a great question. But I love that it was interpreted in many different ways. It could lead to a good classroom conversation, and it makes me consider all sorts of things, not the least of which is standardized assessments. How many times have students gotten the wrong answer for the right reason, because they interpreted an item on a state exam or the SAT differently than the author intended? And how many times have we bored students with antiseptic questions, only because we knew they’d be free from such alternate interpretations? Both scenarios make me sad.