VorkadScandiPuzzl
Visual sequences

Track the Change Between Frames

A sequence is a set of small, steady changes. Name each one separately and the next frame almost draws itself.

Challenge 1 · Moving square

Where does the shading go next?

Difficulty: gentle. One attribute — position — changes each frame.

  1. Frame 1
  2. Frame 2
  3. Frame 3
  4. ?Frame 4
Reveal the answer

The bottom-left square is shaded. The shading moves one square clockwise each frame: top-left, top-right, bottom-right, bottom-left. Frame 5 would return to the top-left.

Challenge 2 · Letter gaps

What letter comes fifth?

Difficulty: moderate. Look at the distance between letters, not the letters themselves.

  1. A1
  2. C2
  3. F3
  4. J4
  5. ?5
Reveal the answer
  1. A to C skips 1 letter (a jump of 2).
  2. C to F is a jump of 3; F to J is a jump of 4.
  3. The next jump is 5: J → K, L, M, N, O.
Macro photograph of a printed strip of symbols on paper with a pencil circling one frame in soft focus
A printed sequence strip in close-up. The working version is always the clear strip on this page.
Challenge 3 · Number pattern

Continue the numbers

Difficulty: moderate. The differences change, but they change steadily.

  1. 2
  2. 6
  3. 12
  4. 20
  5. ?
Reveal the answer
  1. Differences: 4, 6, 8 — rising by 2 each time.
  2. The next difference is 10, so the next term is 30.
  3. Check another way: the terms are 1×2, 2×3, 3×4, 4×5, so the fifth is 5×6 = 30.

When two independent methods agree, you can be confident in the answer.

A method for any sequence

Visual sequence puzzles have a long history in testing and in recreation. John C. Raven's matrices, first published in 1938, made the "what completes the pattern?" question widely familiar. We mention them for their format only; our puzzles are not tests, carry no scores and measure nothing about you. For numbers, the On-Line Encyclopedia of Integer Sequences, begun by Neil Sloane in the 1960s and online since 1996, catalogues hundreds of thousands of patterns — a reminder of how many rules a few terms can hide.

1 · List the attributes

Before predicting anything, name what could change: position, rotation, count, size, shading, colour, the number of sides. Write the list down. In the home-page arrow puzzle, the two attributes were direction and dot count.

2 · Compare neighbours, one attribute at a time

Look at frames 1 and 2 for position only, then frames 2 and 3 for position only. Then repeat for the next attribute. Trying to see everything at once is where most confusion begins.

3 · Describe each rule in a short sentence

"Moves one square clockwise." "Gains one dot." "Jump grows by one." If you cannot state the rule plainly, you may have spotted a coincidence rather than a pattern.

4 · Predict, then check the whole strip

Apply every rule to build the next frame, then confirm the rules hold for all the frames you were given, not just the last two.

Change is easier to see in pairs. Compare two frames, name one difference, and move on.

Common traps

Over-fitting. With only three terms, many rules fit. Choose the simplest rule that explains every frame and that a fair setter would expect you to see. Merging rules. Two simple rules running together can look like one complicated rule. Separate them. Ignoring wrap-around. Rotations and positions often cycle; after the fourth corner comes the first again.

  • Number grids

    From patterns over time to rules across space.

    Work the grid

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