Number memory test average, and what the research actually measured
· 7 min read · Tyamka team
How many digits people repeat back in studies from Miller to Cowan, what the chimpanzee number task measured, and why none of it is a norm for your own score.
If you searched for the average on a number memory test, you probably just repeated a string of digits and want to know if your result is normal. The short answer is that research gives ranges, not a pass mark. In the classic digit task, where you hear or see a string of digits and repeat it, adults usually manage somewhere around seven. When grouping and rehearsal are made hard, estimates drop to about three to five chunks. Our number memory test is a different task. You remember where numbers sit on a grid, not a string of digits, so its levels do not convert into a digit count. Below is what each study measured and how to read your own score.
About seven, the classic number
In 1956 the psychologist George Miller published a paper called "The magical number seven, plus or minus two" in Psychological Review. He collected results from many experiments, including memory span, where a person hears a list of digits and has to say them back in order. Across those studies, adults tended to hold about seven items, give or take two.
Miller himself treated seven as a rough observation, not a law. He also pointed out that the limit is counted in units, not in digits. People can hold more when they group items into bigger units, which he called chunks. A string like 1 9 8 4 2 0 2 6 is eight digits, but if you see it as two years, 1984 and 2026, it is two chunks.
Three to five chunks, the stricter estimate
In 2001 Nelson Cowan published a long review in Behavioral and Brain Sciences titled "The magical number 4 in short-term memory". He argued that when you stop people from grouping and rehearsing, for example by showing items briefly or asking them to repeat a word out loud while they memorise, the limit drops to about three to five chunks.
This does not contradict Miller. A digit span of seven and a limit of four chunks can both be true, because an ordinary digit test lets people group and rehearse the digits. The seven you get on a digit test includes that grouping. The four is closer to what is left when grouping is taken away.
A limit that practice moves
The most famous exception is a study by K. Anders Ericsson, William Chase and Steve Faloon, published in Science in 1980. One student, known in the paper as SF, practised the digit span task for more than 230 hours over many months. His span went from about 7 digits to 79.
The change was narrow. SF was a long-distance runner, and he learned to recode groups of digits as running times he already knew well. That is a skill for this one kind of material. As a later review by Dennis Norris, Jane Hall and Susan Gathercole (Memory and Cognition, 2019) puts it, his span for letters stayed at about seven during the whole training period. So this was very good chunking of digits, not a better memory in general.
A different number task, from a chimpanzee study
Our game is closer to a task from primate research than to digit span. In 2007 Sana Inoue and Tetsuro Matsuzawa of Kyoto University published a short paper in Current Biology called "Working memory of numerals in chimpanzees". Numbers from 1 to 9 appeared at random spots on a touch screen. After a moment they were covered by white squares, and the task was to touch the squares in order from the smallest number up.
In the hardest version, five numbers were shown for 650, 430 or 210 milliseconds before the squares covered them. According to later summaries of the paper (we could not open the original), a young chimpanzee named Ayumu got about 80% of trials right at every duration. The university students tested on the same apparatus did worse as the time got shorter, and at 210 ms they did clearly worse than him.
The result was widely reported as chimpanzees beating humans at memory. Two later studies pushed back. Alan Silberberg and David Kearns (Animal Cognition, 2009) practised the task themselves and reported performance at 210 ms that did not differ from Ayumu's. Peter Cook and Margaret Wilson (Psychonomic Bulletin and Review, 2010) pointed out that Ayumu had much more practice than the human group, and reported that two students, after enough practice, did better than him. So the gap in the original study was at least partly about practice.
What these numbers are not
None of the studies above gives a norm for you. Each one measured a specific task under specific conditions.
| Study | Task | What it found |
|---|---|---|
| Miller, 1956 | Repeat a list of digits or other items | About seven items, plus or minus two, across many experiments |
| Cowan, 2001 | Review of tasks that limit grouping and rehearsal | About three to five chunks |
| Ericsson, Chase and Faloon, 1980, with Norris, Hall and Gathercole, 2019, on letters | Digit span, one student, 230+ hours of practice | From about 7 to 79 digits, while span for letters stayed at about 7 |
| Inoue and Matsuzawa, 2007 | Five numbers on a screen, covered after 650, 430 or 210 ms | A young chimpanzee at about 80% at all durations, humans worse at shorter times |
| Silberberg and Kearns, 2009; Cook and Wilson, 2010 | The same kind of task after practice | Practised humans matched or beat the chimpanzee |
A digit span test online also differs from a lab version in small ways. Some show digits one at a time, some show the whole string at once. Some let you type, some ask you to click. Some add a digit after every success, some start over. Each of these changes the number you end up with, so a span from one site does not compare directly with a span from another.
How our game counts
In Hidden Numbers you see numbers on tiles, tap 1, and the rest hide. Then you tap the hidden tiles in order. On levels 1 to 5 the numbers stay until your first correct tap and grow from 3 to 7. On levels 6 to 10 there are seven numbers and they hide by themselves after 2 seconds, then after shorter and shorter times down to 1 second. On levels 11 to 15 there are eight or nine numbers, shown for 650 ms at first and down to 430 ms at level 15. We did not go below 430 ms, because the chimpanzee study found that untrained people struggle at 210 ms. These level settings are our guess until playtests, not something measured on players.
The result after a level is points, not a span. Each correct tap gives 10 points plus up to 10 for speed, and a wrong tap costs one of three lives. So a score of 90 and a score of 120 on the same level can both mean you remembered every number, one just tapped faster. That is why there is no level where we can say "an average person gets here".
How to read your own result
Compare yourself with yourself. Play the same level a few times on the same device and look at the middle score, not the best. If that middle score moves over a couple of weeks, you have got better at this task. Whether that carries over to anything outside the game is a different question, and we do not claim it does.
If you want to get more out of the game itself, the article on number memory test tips covers grouping and why scores jump between attempts. For a spatial version of the same idea, read about visual working memory, and for sequences, about the sequence memory test average. All three sit under one idea, explained in what working memory is. Other games are on the all games page.