Patterns and Sequences Short Problems: Age 11-14

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Patterns and Sequences: Age 11-14.

We have put together a selection of these short problems as printable worksheets:

Printable worksheets: Age 11-14 ⭐   Printable worksheets: Age 11-14 ⭐⭐   Printable worksheet solutions


  • Small pepper seedlings in orange pots.
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    Street Lamps

    Age
    11 to 14
    Challenge level

    Walking up a steep hill, I pass 10 equally spaced street lamps. How long do I take to walk from the first lamp to the last?

  • Small pepper seedlings in orange pots.
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    Triangular Clock

    Age
    11 to 14
    Challenge level

    Trinni rearranges numbers on a clock face so each adjacent pair add up to a triangle number... What number did she put where 6 would usually be?

  • Small pepper seedlings in orange pots.
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    Expanding Pattern

    Age
    11 to 14
    Challenge level

    How many squares are needed to continue this pattern?

  • Small pepper seedlings in orange pots.
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    Fibonacci Deduction

    Age
    11 to 14
    Challenge level

    Leonard writes down a sequence of numbers. Can you find a formula to predict the seventh number in his sequence?

  • Small pepper seedlings in orange pots.
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    Fruit Line-Up

    Age
    11 to 14
    Challenge level

    This grocer wants to arrange his fruit in a particular order, can you help him?

  • Small pepper seedlings in orange pots.
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    Printing Error

    Age
    11 to 14
    Challenge level

    Every third page number in this book has been omitted. Can you work out what number will be on the last page?

  • Small pepper seedlings in orange pots.
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    Many Matildas

    Age
    11 to 14
    Challenge level

    MatildaMatildaMatil... What is the 1000th letter?

  • Small pepper seedlings in orange pots.
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    What a Coincidence!

    Age
    11 to 14
    Challenge level

    Consider two arithmetic sequences: 1998, 2005, 2012,... and 1996, 2005, 2014,... Which numbers will appear in both?

  • Small pepper seedlings in orange pots.
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    Suit Sequence

    Age
    11 to 14
    Challenge level

    A pattern repeats every six symbols. What are the 100th and 101st symbols?

  • Small pepper seedlings in orange pots.
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    Night Watchmen

    Age
    11 to 14
    Challenge level

    Grannie's watch gains 30 minutes every hour, whilst Grandpa's watch loses 30 minutes every hour. What is the correct time when their watches next agree?

  • Small pepper seedlings in orange pots.
    problem

    Pattern Snake

    Age
    11 to 14
    Challenge level

    This pattern repeats every 12 dots. Can you work out what a later piece will be?

  • Small pepper seedlings in orange pots.
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    Hexagon Line

    Age
    11 to 14
    Challenge level

    How many hexagons are required for the perimeter of the whole shape to have length 1002cm?

  • Small pepper seedlings in orange pots.
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    Sliding Robot

    Age
    11 to 14
    Challenge level

    A robot moves along the number line. Where will it be after 2011 slides?

  • Small pepper seedlings in orange pots.
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    How Many Rectangles?

    Age
    11 to 14
    Challenge level

    By drawing 5 horizontal and four vertical lines, one can form 12 rectangles. What is the greatest number of rectangles that can be formed by drawing 15 lines?

  • Small pepper seedlings in orange pots.
    problem

    Knockdown

    Age
    11 to 14
    Challenge level

    Weekly Problem 51 - 2016
    Pegs numbered 1 to 50 are placed in a row. Alternate pegs are knocked down, and this process is repeated. What is the number of the last peg to be knocked down?

  • Small pepper seedlings in orange pots.
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    Square Grid

    Age
    11 to 14
    Challenge level

    Can you work out what fraction of this grid is shaded?

  • Small pepper seedlings in orange pots.
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    Tiled Floor

    Age
    11 to 14
    Challenge level

    This tiled floor has 109 purple tiles. How many tiles are there altogether?

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    Even Up

    Age
    11 to 14
    Challenge level

    Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

  • Small pepper seedlings in orange pots.
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    Knights and Knaves

    Age
    11 to 14
    Challenge level

    Knights always tell the truth. Knaves always lie. Can you catch these knights and knaves out?

  • Small pepper seedlings in orange pots.
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    Doubly Consecutive Sums

    Age
    11 to 14
    Challenge level

    How many numbers less than 2017 are both the sum of two consecutive integers and the sum of five consecutive integers?

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