QuickenBrain

Number sequence puzzles

Find the next number, fill a grid, or untangle two sequences.

Example

Example

Example

  1. 2
  2. 6
  3. 12
  4. 20
  5. 30
  6. ?

Look for a simple rule that fits every step.

6 questions · Explanation after each answer

6 questions · No time limit

Try six questions.

Look for a simple rule that fits every step.

Help

In Next number, find the rule for one row. In Number grid, each column has its own rule. In Two sequences, alternating terms belong to separate rules. Find the simplest rule consistent with the numbers shown; short sequences can have other continuations. The explanation shows the intended rule.

For Next number, choose one of five answers. For Number grid, type every number in the bottom row. For Two sequences, type the next number. Check your answer, read the explanation, then continue. Keyboard: Tab to the choices or number fields; use the arrow keys to change a multiple-choice selection.

Solving time excludes setup, explanations and background tabs. The optional challenge gives you two minutes of solving time across six questions. When time runs out, unanswered questions count as incorrect. Timed and untimed results stay separate.

The browser loads a complete six-question round from the server when you start or restart. Completed rounds and timed-out challenges are saved when browser storage is available; ending early is not saved. Your individual answers are not uploaded.

This is a practice activity, not a standardized or diagnostic assessment. Results describe only this activity.

Keyboard: press an answer's letter or number to choose it, Enter to check, and Enter again to continue.

Formats: Next number shows one row and offers five answers. Number grid shows rows of numbers where each column follows its own rule, top to bottom; type the whole bottom row, and every right number counts. Two sequences puts two sequences in one row, taking turns; type the number that comes next. In the two typed formats Easy adds or multiplies, and harder levels bring in squares, triangular numbers, primes, two steps in turn, growing gaps and digit rules, with fewer numbers shown at Challenge. The typed formats check for competing rules from the practice’s rule set; a short sequence can still have other mathematical continuations. Each format keeps its own results.

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Number sequence puzzles

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About this practice

Find number patterns by choosing the next term, completing a grid’s bottom row or separating alternating sequences. Each round has six questions with no time limit or an optional two-minute limit; scores count correct answers, or each correct number in a grid.

Find a simple rule that fits every number shown, then use it for the next step. Next number offers 5 answers. Number grid asks you to type a whole bottom row. Two sequences asks for one typed answer after separating the alternating terms. Each round has six questions, with an explanation after every check.

Next number: a worked example

  1. 2
  2. 6
  3. 12
  4. 20
  5. 30
  6. ?
The example shown before you start.
  1. Subtract each number from the one after it. The gaps are 4, 6, 8, 10.
  2. Each gap grows by 2. Continuing that rule gives a gap of 12.
  3. Add it to the last number: 30 + 12 = 42.

A short sequence can have other mathematical continuations. This example uses steadily growing gaps; it does not prove that no other answer is possible. In a round, compare your reasoning with the intended rule in the explanation.

Number grid: follow each column

Column 1Column 2326498??
A shortened setup example. Read down each column.

Column 1 is 3, 6, 9. Adding 3 gives 12. Column 2 is 2, 4, 8. Doubling gives 16. The bottom row is 12, 16. A rule across a row is not needed: each column has its own rule.

Two sequences: separate the positions

  1. 1
  2. 20
  3. 3
  4. 18
  5. 5
  6. 16
  7. 7
  8. ?
A shortened setup example with two alternating sequences.

Positions 1, 3, 5 and 7 contain 1, 3, 5, 7, increasing by 2. Positions 2, 4 and 6 contain 20, 18, 16, decreasing by 2. Position 8 belongs to that second sequence, so the intended answer is 14. Check whose turn comes next before calculating.

What each difficulty changes

  • Next number: Easy uses constant steps, constant factors and growing gaps. Standard adds alternating steps, interleaved counts and multiplying then adding. Challenge uses growing factors, sums of the previous two terms, or alternating multiplication and addition.
  • Number grid: Easy has 2 columns and 5 shown rows, using addition or multiplication. Standard has 3 columns and 5 rows, adding squares, triangular numbers, primes and alternating steps. Challenge keeps 3 columns but shows 4 rows; growing gaps and digit rules replace plain addition and alternating steps.
  • Two sequences: Easy shows 10 numbers using addition or multiplication. Standard shows 9, with squares, triangular numbers, primes and growing gaps also possible. Challenge shows 8, adds digit rules and drops plain addition.

What your result means

Next number and Two sequences count correct answers out of six. Number grid counts each correct bottom-row number, out of 12 on Easy or 18 on Standard and Challenge. A partly correct row earns credit for its correct numbers.

Choose No time limit or the optional 2-minute challenge. The clock counts solving time across the whole round, excluding explanations and background tabs. Unanswered items count as incorrect when time expires. Speed adds no points. Completed rounds and timed-out challenges can be saved; ending early is not saved. Compare the same format, difficulty and timing mode. A result describes those questions, not your general mathematical ability.

For more practice with changing gaps, try Read a number sequence from its gaps.

For a broader mix of practices, explore the math practice test. Sign in free to start a test.

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