Random Digit Generator (0–9)

The smallest random number there is

Every number you’ve ever written is built from the ten digits 0 to 9. A random digit is the atom of randomness: string enough of them together and you can make any random number at all. That’s not just a nice idea. Before computers were everywhere, it was literally how researchers did it.

In 1955, the RAND Corporation published a book called A Million Random Digits with 100,000 Normal Deviates. It’s 400-odd pages of digits generated by an electronic roulette wheel, arranged in blocks of five. Scientists and statisticians used it to pick samples and run simulations. The book still gets reprinted, and its online reviews are some of the funniest on the internet. This page gives you one of those digits at a time, or as many as you ask for.

Codes for games and props

The most common reason people want a run of random digits is a code: a combination for an escape-room padlock, a “secret” number for a treasure hunt, a fake phone extension in a play. Set How many numbers to the code length, untick No repeats (real codes often repeat digits), and generate.

How many codes are possible is easy to work out with digits, since each position has ten options:

Code length	Possible codes	If someone guesses one per second
3 digits	1,000	Under 17 minutes to try them all
4 digits	10,000	Under 3 hours
5 digits	100,000	Just over a day
6 digits	1,000,000	About 11.5 days

For an escape room, three or four digits is plenty, because players should find the clue, not brute-force the lock.

Why humans make bad codes

People are famously predictable with codes. A widely shared analysis by the data blog DataGenetics in 2012 looked at about 3.4 million leaked four-digit PINs and found that 1234 alone made up nearly 11% of them, with 1111 and 0000 not far behind. Codes based on years (19-something) and birthdays were also heavily overused. A random digit generator has no idea what year you were born, which is exactly what you want for a puzzle.

Place value games in the classroom

Random digits are the backbone of a lot of maths lessons with younger kids.

• Biggest number wins. Generate four digits. Everyone arranges them to make the biggest possible number. Then the smallest. Then the closest to 5,000. It sounds simple and it isn’t for an eight-year-old.
• Place value roll. Generate one digit at a time; after each, students decide whether to put it in the thousands, hundreds, tens or units column. They can’t move it later. Highest total wins. It teaches strategy and place value at the same time.
• Decimal practice. Generate three digits and put a decimal point between the first and second. Round to the nearest whole number.
• Number bonds to nine and ten. Generate a digit and pupils shout its partner to make ten.

Probabilities for a single digit

Probability facts for random numbers from 0 to 9

Fact	Value
Possible results	10 (0 to 9, inclusive)
Chance of any one number	1 in 10 = 10%
Even numbers / odd numbers	5 even (50%) · 5 odd (50%)
Prime numbers in range	4 (40% chance of a prime)
Same number twice in 2 picks (repeats on)	1 in 10 = 10%
A chosen number appears at least once in 10 picks	65.1%
Picks until a repeat is more likely than not	5 picks
Average (expected) result	4.5
Average picks to hit one specific number	10

Each digit is exactly 10%. Notice that zero counts as even, so the even/odd split is a perfect five and five. Kids often argue about whether zero is even. It is, because it divides by two with nothing left over.

Zero is the difference

This page exists separately from the 1 to 9 generator because sometimes zero matters and sometimes it’s a nuisance. Use this one when you’re building codes, phone numbers, decimals or anything where 0 is a valid symbol. Use 1 to 9 when a zero would ruin a times-table question or a Sudoku row.

Digits and the random sample

A last, more grown-up use. Suppose you have a list of 100 people numbered 00 to 99 and you need to pick five at random. Generate two digits at a time (first digit for the tens, second for the units), and you’ve got a two-digit number from 00 to 99. Repeat until you have five different ones. That’s exactly how people used the RAND book for decades.

Today, the 1 to 100 page does it in one step. But building a number from digits by hand is a nice way to show students that any random number can come from simple pieces, and that’s worth ten minutes of a statistics lesson.

Digits in a dice-free board game

Lots of homemade games need a ten-sided outcome and nobody owns a d10. Map the digits onto your game instead. A few we’ve used:

• Movement with a twist. Move the number of spaces shown, but a 0 means you lose your turn. Tense, especially near the finish.
• Card-free poker practice. Five random digits form a “hand.” Pairs, three of a kind and straights all exist (0 to 4 counts as a straight). It’s a sneaky way to practise thinking about probability.
• Colour by digit. Assign ten colours to the ten digits and generate a sequence for a beaded bracelet or a pixel pattern. Every bracelet comes out different.

How evenly do digits really fall?

If you generate 100 digits, you won’t get exactly ten of each. A typical run gives something like seven of one digit and thirteen of another, and that’s fine. Statisticians test whether a sequence is “random enough” with a chi-square test that compares the counts to ten each; a spread like seven to thirteen passes easily. Kids sometimes see a lopsided tally and decide the generator is broken. Running it again with 1,000 digits and seeing the counts settle much closer to 100 each is the best answer.

And if a game needs a “lucky” digit drawn by each player, ten players can each get their own with No repeats ticked and How many numbers set to 10.