Number Detective Puzzle Rules and How to Solve Them

Summary: A Number Detective puzzle gives you a chart of numbers and a short list of clues such as “Even”, “Less than 25” or “Divisible by 8”. Cross out every number a clue rules out, and the number left standing is the culprit. Most puzzles have two to four clues, and starting with the clue that clears the most numbers is the fastest way in.

Want to make your own? The Number Detective puzzle generator creates them with answer keys, ready for print.

A Number Detective is a number elimination puzzle with a detective twist. Every number on the chart — often 1 to 100 in ten rows — is a suspect. Each clue is a witness statement that clears some of them. Put all the statements together and only one number fits every one of them: that is the culprit.

A Number Detective puzzle: the numbers 1 to 100 in a ten-by-ten chart, with the clues Less than 25, Divisible by 8 and Ends in 4

The Goal

Find the one number on the chart that matches every clue. On the puzzle above, the culprit is less than 25, divisible by 8 and ends in 4. Try it before you read on; the steps below crack it in three quick moves.

Some puzzles are set the other way round, as a find-all page: the heading reads “Find ALL numbers that are:” instead of “Find the ONE number that is:”, and two to ten numbers survive the clues. The rules are the same; you simply circle every survivor instead of one.

Number Detective Rules

Each clue is a fact about the answer. A number that breaks a clue cannot be the answer, so it is crossed out. A number that passes every clue stays.
Clues read literally. Greater than 30 means 31 and up — 30 itself is out. Less than 25 means 24 and down. Between 20 and 25 includes both ends, so 20 and 25 both count.
Digit clues look at how the number is written. Ends in 4 is the last digit. Tens digit is 6 is the second digit from the right, so it matches 61 and also 160; numbers below 10 have a tens digit of 0. Has 2 digits counts digits, and Digits add up to 9 adds them: 9, 18, 27, 36, 45 … 90 — but not 99, whose digits add up to 18.
Number-family clues mean what a maths teacher means. Divisible by 8 leaves no remainder. Prime means exactly two divisors — so 1 is not prime, and 2 is. A square number is 1, 4, 9, 16 and so on. Has a repeated digit means some digit appears more than once: 33, 100, 101 and 111 all qualify.
Every clue matters. No clue in a Number Detective puzzle is filler: each one clears at least one number that all the other clues would let through. So if a clue seems to do nothing, read it again.
No clue kind appears twice. You never get two Greater than clues on one puzzle, though Greater than and Less than can appear together to fence in a range.

How to Solve a Number Detective: Four Steps

Start with the clue that keeps the fewest numbers. Clues do not have to be used in order — the answer is the same whichever way round you take them. Estimate each clue’s reach before you cross anything out: Ends in 4 keeps one number in ten, Divisible by 8 about one in eight, Less than 25 about a quarter of a 1 to 100 chart. Start with Ends in 4: only ten numbers on the chart end in 4 (4, 14, 24 … 94), so ninety are gone in one move.
Work the shortlist, not the chart. Once a strong clue has done its job, stop scanning the whole grid and test the survivors one by one. Less than 25 turns 4, 14, 24, 34 … 94 into just 4, 14 and 24.
Finish with the fussy clue. Divisibility and prime clues are slow to check across a whole chart and quick to check on three numbers. 4 and 14 are not divisible by 8; 24 is. The culprit is 24.
Check the culprit against every clue. Run the survivor past the full list once more. 24 is less than 25, divisible by 8 and ends in 4 — case closed.

Solved Number Detective puzzle: 24 circled in red on a 1 to 100 chart, with the answer printed under the clues

Crossing out on paper? Strike lightly so the numbers stay readable — a struck-out number is still useful when you double-check.

The Four Levels

The level sets which kinds of clue appear and how many you usually get:

Very Easy — 2 clues: even or odd, greater than, less than, between, ends in.
Easy — 3 clues: the same kinds as Very Easy.
Medium — 3 clues: adds divisible by, not divisible by, tens digit and number of digits.
Hard — 4 clues: adds prime, not prime, square numbers, digit sums and repeated digits.

From Easy up, a small or patterned chart can get one clue fewer, because every clue on the page has to pull its weight.

A Very Easy page is a two-step case for a young solver: on the chart of 1 to 50 below, Greater than 40 leaves 41 to 50, and Ends in 3 leaves just one — 43.

A Very Easy Number Detective: the numbers 1 to 50 with the clues Greater than 40 and Ends in 3

At Hard, the clues get cleverer as well as longer. On the case below, start with Has a repeated digit: it leaves only 11, 22, 33 … 99 and 100. Greater than 30 cuts that to 33, 44 … 99 and 100, Odd to 33, 55, 77 and 99, and Less than 50 leaves 33. Some puzzles add a bonus question under the clues, “Which clue eliminated the most numbers?”, and print its answer on the solution. Answer it before you start crossing out: the printed answer counts how many numbers each clue rules out on its own, across the whole chart, and that clue is usually the strongest place to start.

A Hard Number Detective solved: 33 circled, with the bonus question and its answer, clue 2, printed under the clues

Find-all pages work the same way at every level. Here Ends in 7, Greater than 20 and Less than 50 leave three numbers — 27, 37 and 47 — and the solver circles all of them.

A find-all Number Detective solved: 27, 37 and 47 circled

Charts are not always 1 to 100. A chart can be any run of numbers, a hand-picked list, or a pattern such as every multiple of 7 — the same clues, a different set of suspects.

Try It Online

In the browser you solve by elimination: pick a clue, then click the numbers it rules out. Each one turns light grey, and the clue keeps count of how many it has removed. Strike a number the selected clue does not rule out — even if another clue does — and it flashes red and stays put, so select the right clue first; click a struck number to bring it back. A Remove all for this clue button clears the rest in one go. When only the answer is left standing (or, on a find-all page, the answers), each gets its red circle. Play Number Detective in your browser — nothing to download. The general player controls — checking your answer, resetting, the timer, and working through a set — are covered once in How to Play Puzzles Online.

FAQ

Can a Number Detective have more than one answer?
A page headed “Find the ONE number that is:” has exactly one, and every clue is needed to get there. Find-all pages, headed “Find ALL numbers that are:”, have two to ten answers instead, and you circle them all.

Do I have to use the clues in order?
No. The answer is the same whichever order you take them in, and starting with the clue that keeps the fewest numbers is usually fastest.

Is 1 a prime number?
No. A prime has exactly two divisors, and 1 has only one, so a Not prime clue keeps 1 and a Prime clue crosses it out. The smallest prime is 2.

Does “greater than 30” include 30?
No — it means 31 and up, and Less than works the same way. Between is the one that includes both ends.

Who are Number Detective puzzles for?
Anyone who likes a quick deduction. Very Easy two-clue cases suit early number work; Hard cases with primes, square numbers and digit sums give adults a proper think, and the bonus question turns any page into a strategy lesson.

Make Your Own Number Detective Puzzles

You know how the case comes together — now make your own, from two-clue warm-ups to four-clue Hard cases, each with its answer key and ready for a puzzle book, a worksheet pack or a maths lesson.

Create your own Number Detective puzzles with the Number Detective generator

Not ready yet? Try the free demo first — it covers every module.

How Number Detective Puzzles Work