Patterns and Sequences Short Problems: Age 14-16

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Patterns and Sequences: Age 14-16.

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

Printable worksheets: Age 14-16 ⭐⭐   Printable worksheet solutions


  • Small pepper seedlings in orange pots.
    problem

    12345

    Age
    14 to 16
    Challenge level
    2 out of 3

    Repeat a pattern of numbers to form a larger number. Can you find the sum of all the digits?

  • Small pepper seedlings in orange pots.
    problem

    Below 400

    Age
    14 to 16
    Challenge level
    2 out of 3

    Can you work out which number will appear directly below 400 in this pattern?

  • Small pepper seedlings in orange pots.
    problem

    Alternating Sum

    Age
    14 to 16
    Challenge level
    2 out of 3

    Given that the number 2008 is the correct answer to a sum, can you find n?

  • Small pepper seedlings in orange pots.
    problem

    Newspaper Sheets

    Age
    14 to 16
    Challenge level
    2 out of 3

    From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?

  • Small pepper seedlings in orange pots.
    problem

    Collatz 13

    Age
    14 to 16
    Challenge level
    2 out of 3

    If a number is even, halve it; if odd, treble it and add 1. If a sequence starts at 13, what will be the value of the 2008th term?

  • Small pepper seedlings in orange pots.
    problem

    Collatz-Ish

    Age
    14 to 16
    Challenge level
    2 out of 3

    A sequence is generated using these rules. For which values of n is the nth term equal to n?

  • Small pepper seedlings in orange pots.
    problem

    Trolley Park

    Age
    14 to 16
    Challenge level
    2 out of 3

    In a supermarket, there are two lines of tightly packed trolleys. What is the length of one trolley?

  • Small pepper seedlings in orange pots.
    problem

    Diagonals

    Age
    14 to 16
    Challenge level
    2 out of 3

    How many diagonals does a regular icosagon (20 sides) have?

  • Small pepper seedlings in orange pots.
    problem

    Difference Sequence

    Age
    14 to 16
    Challenge level
    2 out of 3

    When will 2000 appear in this sequence?