PT Puzzle: Tricky Fingers

A riddle to challenge your head and hands.

By Andrea Bartz, published on September 6, 2011 - last reviewed on June 9, 2016

This tactile riddle challenges your head and hands. It improves concentration and works your body sense—the ability to feel where your fingers are in space. "It's not a common expertise in our culture," says designer Scott Kim. As a pianist, he's used to keeping track of his digits, and an athlete or Tai Chi practitioner might have a good read on how their body moves. But for most of us, this puzzle targets an underutilized part of the brain. Touch and go! —Andrea Bartz

 Visuals of a hand puzzle

Touch your fingers together as shown in Figure 1, so the thumb, the pointer, and the middle finger of one hand touch the corresponding fingers of the other hand. We'll call this the starting position.

Now touch the same three fingers of each hand together in a different order. For instance, in Figure 2 I have kept my middle fingers together and switched my thumb and second fingers. This move—keeping one pair of fingers the same and switching the others—is called a swap move.

Challenge 1: In how many different ways can you touch the first three fingers of one hand to the first three fingers of the other hand? Hint: The answer is less than 10.

Challenge 2: Move through all the finger-touching positions you found in the Challenge 1 by making a series of swap moves. Start by putting your hands in the starting position shown in Figure 1, above. Swap your first and second fingers, as shown in Figure 2. Continue making swap moves, each time reaching a new position, until you've made all the possible positions. Hint: From the last position, you can make a swap move to get back to the starting position.

If the two challenges at left make your heart rate quicken, you're not alone. "You'll need courage just to try this," says designer Scott Kim. "That's the most basic thing about puzzles: It's not the technique itself that determines success, it's a willingness to try."

So take a deep breath. Challenge 1 is really a mathematical problem: Each configuration can be written as a series of numbers, so it becomes a different question—how many orders are there to put the numbers in?

You use your parietal lobe to painstakingly count up the unique positions, explains neuroscientist Richard Restak. And your motor cortex gives orders to your fingers as they bend, stretch, and touch.

The second challenge builds on the first; if you've jotted down all the combinations, you can essentially check 'em off as you move through them. There's a simple trick to not accidentally repeating a position—a trick you'll need to figure out.

Your body takes a tactile snapshot each time your hands reach another position. This is motor memory, a mental calisthenic that taps memory-based areas such as the hippocampus and the movement-based motor cortex. "Each time you move,"Restak says, "you're not envisioning but actually feeling whether your hands have been in that position before."

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



Dean Drobot/Shutterstock


1. The first three fingers of each hand can touch one another in six ways. We can write down the positions by recording which right-hand finger each of the three left-hand fingers touch. (Assume the left hand is still and think of your right-hand thumb as 1, pointer as 2, and middle finger as 3.) The six positions are: 123, 132, 213, 231, 312, 321.

2. Here's one way to do it: Starting from the two positions shown in the puzzle, the sequence of six positions is: 123, 213, 312, 321, 231, 132. There are many other solutions. The trick: Don't swap the same two fingers twice in a row.