How many digits can you remember?

In 1956 the psychologist George Miller published a paper whose title became one of the most quoted in the field: "The magical number seven, plus or minus two". He brought together experiments showing that people can hold about seven items in immediate memory, whether the items are digits, letters or words. For digits, he wrote, "we can recall about seven of them".

Miller noticed something surprising. The limit didn't depend on how much information each item carried. A binary digit, 0 or 1, carries far less than a decimal digit, yet people could repeat back about nine binary digits and about eight decimal ones. "Immediate memory", he wrote, "is limited by the number of items."

His paper actually covered two different limits that both happen to land near seven. One is absolute judgment: how many categories you can tell apart, such as different pitches of a tone. The other is immediate memory. "Absolute judgment is limited by the amount of information", Miller wrote, while immediate memory is limited by the number of items.

He was careful not to make too much of the number itself. Near the end of the paper he suggested that the seven turning up again and again might be "only a pernicious, Pythagorean coincidence".

Later researchers argued that the true limit is smaller. In a 2001 review, Nelson Cowan brought together a wide range of studies and concluded that when people can't rehearse items or group them together, they hold about three to five chunks at once, around four on average.

Cowan argued that Miller's seven "was meant more as a rough estimate and a rhetorical device than as a real capacity limit".

To see that smaller limit, researchers have to stop people from chunking. Cowan describes several ways, including giving people more information than they can group, and taking other steps to block the recoding of items into larger chunks. Under those conditions, rehearsal and long-term memory can't combine the items into bigger units, and what's left averages about four.

One way to fit the two numbers together: seven is roughly what people manage in an everyday digit test, where they can repeat the digits under their breath and group them without trying. Four is closer to what is left when those tricks are blocked.

Cowan ties that limit to the focus of attention: roughly how many separate things you can keep in mind at the same moment.

Miller's most useful idea was the chunk: a group of items your memory can treat as a single unit. The digits 1, 9, 8 and 4 are four items, but if they make you think of a year, they become one chunk.

This is why long numbers are so often written in groups. 415 555 0123 is far easier to hold than 4155550123, even though the digits are the same: three chunks instead of ten separate digits.

Miller called this process recoding. He described experiments by Sidney Smith in which strings of binary digits were read in groups, with each group translated into a single number. With that recoding, Smith could hold far more binary digits than the usual nine.

Say the game shows 19846207. Read digit by digit, that's eight separate items, right at the edge of the usual limit. Read as 1984 (a year), 62 (an age) and 07 (July, the seventh month), it's three chunks, comfortably inside it.

The meanings don't have to be clever. They just have to mean something to you. A bus route, a friend's birthday or the last digits of an old phone number all work. What matters is turning several digits into one thing you already know.

Chunks help when you type the number back, too. You only need to keep three things in order, then unpack each one as you go.

The most famous demonstration of chunking comes from a 1980 study by K. Anders Ericsson, William Chase and Steve Faloon. After more than 230 hours of practice in the lab, their volunteer, known as S.F., increased his digit span from 7 to 79. On other memory tests with digits, the study reports, his performance equaled that of memory experts with lifelong training.

What changed was not a bigger memory but a better system. S.F. was a keen runner, and he learned to see groups of digits as running times: a string like 3492 could become 3 minutes 49.2 seconds, a very fast mile. Then he arranged those groups into larger groups that he could recall in order.

The study's summary puts it plainly: "With an appropriate mnemonic system, there is seemingly no limit to memory performance with practice."

Our number memory game is a cousin of the classic digit span test, with a few differences worth knowing.

• You see the number rather than hear it. Many classic versions read the digits aloud, one at a time. Seeing the whole number at once makes it easier to split it into groups.
• The number stays on screen longer as it grows. The first round shows 3 digits for 2.2 seconds, and each level adds a digit and about two-thirds of a second.
• You type the number back, so a slip of the finger counts as a mistake.
• One mistake ends the run, and your score is the longest number you got right.

Our bands follow the research loosely. Typical Span covers 6 to 8 digits, right around Miller's seven. Past that, you were probably grouping the digits, whether you meant to or not, which is why the next band, for 9 to 11 digits, is called Chunker.

Further up, Long Hold covers 12 to 15 digits, and anything past that is called Unreasonable: the kind of span that usually takes a practiced memory system, like the one S.F. built.

• Split the number into groups of three or four as soon as you see it.
• Use the whole display time. The number stays up longer as it grows, so there's time to split it into groups before it disappears.
• Give a group a meaning where you can: a year, a time, a price, or part of a number you already know.
• Repeat the groups to yourself in a steady rhythm until you start typing. Rehearsing them in your head helps keep them from slipping.
• Type steadily, group by group, rather than racing.

This is a game. A score on one try, on one device, shows how you did in that moment. It isn't a measure of your memory in general, and it says nothing about your health.