Sequences often have a simple rule, but a few examples can fit several patterns. The explanations here describe the intended pattern for each challenge.
How it works: Read the problem, open a hint only if you need one, then reveal the answer when you're ready.
PatternsMedium
Growing letter gaps
What comes next in this sequence of letters: A, C, F, J, O, …?
First hint
Count how many positions you skip each time.
Second hint
The jumps are +2, +3, +4, +5.
Reveal answer and explanation
UThe next jump is six places: O → U.
PatternsHard
Square within square
How many squares of all sizes appear in a 4 × 4 square grid?
First hint
Include larger squares as well as the smallest cells.
Second hint
Count 1 × 1, 2 × 2, 3 × 3 and 4 × 4 squares.
Reveal answer and explanation
30 squaresThere are 16 single-cell squares, 9 two-cell-wide squares, 4 three-cell-wide squares and 1 large square: 16 + 9 + 4 + 1 = 30.
PatternsEasy
Perfect squares
Find the next number: 1, 4, 9, 16, 25, …
First hint
Think about multiplying numbers by themselves.
Second hint
These are 1² through 5².
Reveal answer and explanation
36The next square number is 6² = 36.
PatternsMedium
Staircase pattern
Find the next number: 2, 6, 12, 20, 30, …
First hint
Look at the differences.
Second hint
They increase by 4, 6, 8 and 10.
Reveal answer and explanation
42The differences rise by two each time. Add 12 to 30 to get 42.
PatternsMedium
Double and subtract
Find the next number: 5, 10, 8, 16, 14, 28, …
First hint
Two different operations alternate.
Second hint
First double, then subtract two.
Reveal answer and explanation
26The series alternates ×2, −2. After 28, subtract 2 to get 26.
PatternsEasy
A week of clues
What comes next: SUN, MON, TUE, WED, THU, …?
First hint
They are abbreviations.
Second hint
Think of the seven days.
Reveal answer and explanation
FRIThe sequence gives the days of the week in order.
PatternsEasy
Quarter turn
An arrow points north, east, south, west, north, … Which direction comes next?
First hint
Each move turns the same amount.
Second hint
Rotate the arrow clockwise through 90°.
Reveal answer and explanation
EastEach arrow is a quarter-turn clockwise from the previous one.
PatternsEasy
Number rows
Complete the missing entry: Row 1: 2, 4, 8. Row 2: 3, 6, 12. Row 3: 5, 10, ?
First hint
Each row follows the same rule.
Second hint
Double to move from one entry to the next.
Reveal answer and explanation
20In every row, each entry is twice the entry to its left: 5, 10, 20.
PatternsHard
Painted cube
A 3 × 3 × 3 cube is made from 27 small cubes. You paint every outside face, then separate them. How many small cubes have paint on exactly two faces?
First hint
Look at the edge cubes.
Second hint
Exclude the eight corner cubes.
Reveal answer and explanation
12 cubesEach of the 12 edges has one middle cube touching exactly two exposed faces.
PatternsMedium
Increasing differences
Find the next number: 2, 3, 5, 8, 12, …
First hint
Subtract each number from the next.
Second hint
The differences are 1, 2, 3 and 4.
Reveal answer and explanation
17The next difference is 5, giving 12 + 5 = 17.
