Random sequence generation

How it works

You name two ends of a closed interval of integers. The generator takes each integer from the lower end through the upper end exactly once and returns those values in an unpredictable order. That is a shuffle of the interval, like cards dealt from a deck that is not put back. The length of the list is the size of the interval. You do not ask for “five numbers from 1 through 10” on a true sequence and still expect every integer in 1 through 10; that request is a sample, and it belongs on a different control.

People also look for a random number generator sequence, a random number sequence generator, or a random org sequence generator when they want this shuffle. The wording changes. The job does not: unique values, full coverage of the span, one permutation. RANDOM.ORG’s sequence form is the well-known public example of the same idea, built from its noise stream rather than from a language’s ordinary rand. A programming language can shuffle a list too. That shuffle is only as honest as the algorithm and the seed. Do not mix those claims.

Inclusive ends are the usual reading. If you asked for 1 through 20, both 1 and 20 must appear, each once. If a value is missing, the interval was wrong, the tool sampled instead of shuffling, or the output was truncated in the copy step. Check the printed bounds against the printed list before you blame chance. Chance does not eat a number in a permutation of a finite set.

The generator does not know what the integers stand for. Encoding people as 1 through n is your mapping. Keep that mapping written down beside the list, or you will not be able to say who was first when the integers are all you saved.

A sequence is a shuffle, not a handful of rolls

A stream of independent draws allows duplicates. Two sixes in a row can be honest on a die. A sequence of 1 through 6 cannot contain two sixes, and it cannot omit 4. If your classroom needed unique tickets, the sequence is the right object. If you needed dice, it is the wrong object. Mixing them and then arguing about fairness is how a draw turns into a grievance.

Write the inclusive minimum and maximum. Confirm you want every integer in that span once. Generate the permutation and copy the whole list, not a glance at the first line. Save the bounds with the list. A lonely shuffle without ends is not a specification.

If you already have names, shuffle the names. Do not translate people into numbers unless you must, and if you must, publish the translation. A sequence of integers is easy to audit when the span is public. It is easy to cheat when someone later says “7 meant a different person.”

Short spans repeat their small world: a shuffle of 1 through 4 has only so many looks. That is combinatorics, not a broken button. Long spans produce long lists. If you needed ten unique values from a thousand, that is a sample without replacement, which is a take from a shuffle, not the full sequence. Say which one you wanted before you click.

When the permutation is the wrong object

It is the wrong object for a secret key. It is the wrong object if you will discard values you dislike after you see them: throwing out 8, 9, and 10 from a 1-through-10 shuffle is not a fair 1-through-7. Set the span you meant. It is the wrong object if the group cannot see the same output and you later need to prove the order. Paste the bounds and the full list into the record the group already uses.

A sequence that quietly drops a number is a marked deck. Print the whole list, then argue. Do not reroll because the first value “felt” unlucky. The first value is one card from a shuffled deck. The fairness lived in the shuffle and in the published span, not in your taste after the fact. If you needed a different span, say so before the next draw, and make that a new sequence, labeled as new.