## Archive for February 11, 2016

### Mathematically Unconscious

Both of my sons sleepwalk. At least once a week, one of them will wake up an hour after bedtime, walk down the stairs, and start speaking gibberish. They have no idea what they’re saying, because they aren’t awake — even though their eyes are open. (Freaky!)

During a recent somnambulation, Alex stood at the top of the stairs. He appeared frustrated. Finally, he said:

I just need to find the numbers. It shouldn’t take long.

As you might well imagine, it’s a little scary to have your son walking and talking while asleep. The only solace is that his subconscious thoughts are about math.

I don’t sleepwalk. But I recently had a dream in which I attended a cocktail party and asked the other attendees a most unusual question:

I suspect that my 7 years as an editor and 4 years as a question writer for MathCounts are to blame, but that doesn’t make it any easier to accept.

I vividly remember a dream I had in college, on the night prior to my Linear Algebra midterm. Feeling unprepared for the exam, my nightmare consisted of two brackets pinching my head like a vice, while numbers floated past.

I awoke in a cold sweat at 5 a.m., and proceeded to a study carrel for more test prep.

I was happy to learn that other folks dream about math, too. While subscribed to a listserve for former instructors of the Center for Talented Youth, I received a message from Mark Jason Dominus that read, “I dreamt of the following problem while I was sleeping last night. When I woke up, I convinced myself that it was a good problem, so I’ve decided to share it.”

The volume of a 3 × 3 × 3 cube is 27 cubic units, and the volume of a 2 × 2 × 1 rectangular prism is 4 cubic units. Theoretically, six prisms should be able to fit inside the cube, with three cubic units empty. But can you arrange six 2 × 2 × 1 prisms so they fit inside a 3 × 3 × 3 cube?

Good luck, and sweet dreams!