PT Puzzle: Mental Blocks

Challenge your spatial thinking abilities with this brainteaser

By Andrea Bartz, published on November 1, 2011 - last reviewed on June 9, 2016

 Tetris shapes

"Unless you're a surgeon or an architect," says neuroscientist Richard Restak, "you probably don't do much spatial thinking." Our society favors words and concepts—not the kind of abstract visual reasoning required to pull off this brainteaser. —Andrea Bartz

 Tetris shapes

The Challenge

: Shown at the left are the seven shapes that appear in the video game Tetris. Each shape is made of four squares. Notice that two pieces are mirror images of two other pieces: The blue L mirrors the gold L, and the green S mirrors the red Z. If we ignore mirror-image duplicates, there are five distinct Tetris shapes.

Tetris's creator, Alexey Pajitnov, based his game on pentominoes, a mathematical puzzle. Pentominoes are shapes made of five squares. How many distinct pentominoes are possible, ignoring mirror-image duplicates?

This is no one-shot, Eureka!-punctuated puzzle—it's challenging and gives your spatial thinking a thorough workout. Few people could do this one mentally, so grab some supplies: You could cut out five squares and slide them around, or just use pen and paper to draw out different block configurations.

The key is finding a methodical approach. "It's important not just to come up with a system, but to make sure it's a system for generating all the solutions," says puzzle designer Scott Kim. He started with a shape that had five blocks in a row. Then he chopped it down to a four-in-a-row base and corkscrewed around the extra piece, tossing out mirror-image duplicates as they appeared. Next came shapes with three blocks in a row and two floating, and then two in a row and three moving. "It's a little messy," he says, "but it's systematic."

Watching for mirror-image shapes feels difficult, but "seeing things in reverse is quite natural for humans," Restak says. As anyone who's ever taken an aerobics class will tell you, when someone facing you (e.g., an instructor) tells you to copy her movement and then steps to her right, you instinctually want to mirror her on your left foot.

Your frontal lobe keeps you focused as your right parietal lobe (home of visuospatial processing) rotates the figures and counts them up.

Pajitnov used pentomino shapes in early versions of Tetris, but he quickly realized that players would have difficulty holding so many different shapes in memory and toggling the right ones into place. "As a responsible game designer, he tried the next level and found that four building blocks work really well," Kim says. The human brain can comfortably hold about seven ungrouped items in working memory at once—and conveniently, Tetris gamers play with that many shapes.

Puzzle adapted from The Playful Brain by Richard Restak and Scott Kim (Riverhead Books, 2010)