Twelve number sequences with blanks to fill in, six easy and six medium, all on this one page. Every row follows one of five pattern families, and a script checked each row so the missing numbers land only one way. Hit Ctrl+P (Cmd+P on Mac) to print, solve with a pencil, and open the solution blocks only when a row has you stuck. No download, no email, no sign-up.
How to use this page: solve on screen or on paper. The solution blocks stay collapsed until you tap them, so no accidental spoilers while you work. If you want grid-style number puzzles instead of rows, the number puzzles for adults page works the same way with fill-in grids.
Puzzle 1 — Six Easy Rows Easy
The five families
Each row follows exactly one of these patterns. The printed numbers pin down which one.
Same step: add or subtract the same number every move (4, 7, 10, 13...)
Same multiple: multiply or halve every move (3, 6, 12, 24...)
Growing steps: the gap itself grows by a fixed amount, like gaps of 1, 2, 3, 4 or 3, 5, 7, 9
Two tracks: the odd and even positions each run their own add-or-subtract line (1, 20, 3, 18.)
Build-up: each number is the sum of the two before it (1, 1, 2, 3, 5...)
Fill in the six empty cells.
4
7
10
13
22
25
40
36
32
24
16
12
1
2
4
7
22
29
2
10
4
12
6
8
5
9
13
25
29
33
1
1
2
3
5
21
Solutions for the six easy rows
4
7
10
13
16
19
22
25
40
36
32
28
24
20
16
12
1
2
4
7
11
16
22
29
2
10
4
12
6
14
8
16
5
9
13
17
21
25
29
33
1
1
2
3
5
8
13
21
Row 1: same step, +3 each move. The blanks take 16 and 19.
Row 2: same step, −4 each move. The blanks take 28 and 20.
Row 3: growing steps. The gaps run 1, 2, 3, 4, 5, 6, 7, so the blanks take 11 and 16.
Row 4: two tracks. Positions 1, 3, 5, 7 climb 2, 4, 6, 8 and positions 2, 4, 6, 8 climb 10, 12, 14, 16. The blanks take 14 and 16.
Row 5: same step, +4 each move. The blanks take 17 and 21.
Row 6: build-up. Each number is the sum of the two before it: 8, then 13.
Puzzle 2 — Six Medium Rows Medium
Rules
Same five families as above. These rows lean on multiplication, halving and mixed tracks, and two of them change direction mid-row.
Fill in the thirteen empty cells.
3
6
12
48
192
384
128
64
16
4
1
2
3
5
8
21
55
1
20
3
18
5
16
1
4
9
25
49
64
2
3
5
8
12
23
Solutions for the six medium rows
3
6
12
24
48
96
192
384
128
64
32
16
8
4
2
1
2
3
5
8
13
21
34
55
1
20
3
18
5
16
7
14
1
4
9
16
25
36
49
64
2
3
5
8
12
17
23
30
Row 1: same multiple, ×2 each move. The blanks take 24 and 96.
Row 2: same multiple, halve each move. The blanks take 32, 8 and 2.
Row 3: build-up. Each number is the sum of the two before it: 13, then 34.
Row 4: two tracks, moving apart. Positions 1, 3, 5, 7 climb 1, 3, 5, 7 and positions 2, 4, 6, 8 fall 20, 18, 16, 14. The blanks take 7 and 14.
Row 5: growing steps with gaps of 3, 5, 7, 9, 11, 13, 15, which is the square numbers 1² through 8². The blanks take 16 and 36.
Row 6: growing steps with gaps of 1, 2, 3, 4, 5, 6, 7. The blanks take 17 and 30. This row reads as build-up (2, 3, 5, 8, then 13) right up until the printed 12 kills that reading. That is the trap, and it is why the rule says to check every printed cell before you commit.
How to solve a number sequence in 3 steps
Read the row and mark the gaps between printed cells. Two blanks in a row mean you lean on the end cells; a blank between two givens usually falls out in one move.
Test the families in order: same step first, then growing steps, then two tracks, then build-up, then same multiple. The first family that fits every printed cell wins. If two families seem to fit, hunt for a cell that separates them, like the printed 12 in row 6 above.
Write your fills, then re-read the finished row against the family. A pattern that explains three cells can still break at the fifth, and the re-read catches it for the cost of ten seconds.
Four opinions from building these
(Opinion.) Solve the rows out of order. Start with the row where printed cells sit closest together. Momentum from one quick win carries you through the stubborn rows better than row order does.
(Opinion.) Pencil small guesses above the blanks. Holding two candidate gaps in your head while you check the next cell is where copying errors start. Let the paper carry them and erase as cells resolve.
(Opinion.) Print the page instead of solving on screen. A paper copy lets you cross out a whole family with one pencil line and keep the sheet as scratch work. On screen that all happens in your head, which is the weaker place for it.
(Opinion.) Skip the timer on the Medium set. Halving and two-track rows reward staring. A clock pushes people into arithmetic slips on exactly the rows that punish them hardest.
Checked by a script before publishing
Every row on this page went through a short Python script before it went up. The script builds every sequence the five families can produce (same step, same multiple, growing steps, two tracks, build-up), keeps the ones that match the printed cells, and counts the distinct fills. All twelve rows came back with exactly one fill. Three Easy rows answer to two family names at once, because a straight +3 line is also two parallel tracks moving together, but both readings produce the same numbers. No row on this page has two answers. If you want the same build discipline applied to full puzzle books, that is what the pack below is.
Want 30 more? Case Files: Quick Cases
The paid pack wraps thirty cases in a detective frame from the Grayharbor night desk. Five kinds of detective work, full answer keys at the back for A4 and Letter PDFs both included. Same promise as this page: one answer per case, checked rather than assumed.
“A printable puzzle book from the Grayharbor Detective Agency night desk. Thirty case files, five kinds of detective work, full answer keys at the back. Pick your paper size, print, sharpen a pencil. No app, no login, no subscription.”
— from the pack’s readme
“Every case has exactly one answer. The puzzles were generated solution-first: the answer was fixed, then clues were chosen and checked by a solver so the printed statements allow only that one solution.”
— from the pack’s readme
“Print at 100% / “Actual size”. The files already carry the right page size, so don’t scale-to-fit.”
Caesar shifts, atbash, keyword ciphers, number codes
21-25
Witness Matches (cases 019-023)
Statements from a scene, match each person to what they carried and where they stood
26-30
Timelines (cases 024-028)
Six events, rebuild the order from time clues
31-32
Final Cases (cases 029-030)
Five suspects, one thief, profile table plus statements
33-34
Answer Keys
Full solutions for all 30 cases
One honest note: the sequence rows above are built with the same method but they are not pages from the book. The book’s thirty cases are detective work, not sequence fills, and the table above shows exactly what you would get.