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Secondary live problems and recent solutions

Each time you visit the NRICH site there will be some activities which are 'live'. This means we are inviting students to send us solutions, and we will publish a selection of them, along with each student's name and their school, a few weeks later. If you'd like to know more about what we're looking for, read this short article.

The last day for submitting solutions to these live problems is Monday 28 April.

Live problems

  • Climbing Complexity
    problem

    Climbing complexity

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    In the 2020 Olympic Games, sport climbing was introduced for the first time, and something very interesting happened with the scoring system. Can you find out what was interesting about it?

  • Charlie's delightful machine
    problem

    Charlie's delightful machine

    Age
    11 to 16
    Challenge level
    filled star empty star empty star

    Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Recently solved problems

  • Keep it simple
    problem

    Keep it simple

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Can all unit fractions be written as the sum of two unit fractions?

  • Finding factors
    problem

    Finding factors

    Age
    14 to 16
    Challenge level
    filled star empty star empty star

    Can you find the hidden factors which multiply together to produce each quadratic expression?

  • Shifting Times Tables
    problem

    Shifting times tables

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Can you find a way to identify times tables after they have been shifted up or down?

  • Cuboid challenge
    problem

    Cuboid challenge

    Age
    11 to 16
    Challenge level
    filled star filled star empty star

    What's the largest volume of box you can make from a square of paper?

  • Take Three From Five
    problem

    Take three from five

    Age
    11 to 16
    Challenge level
    filled star filled star empty star

    Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

  • Slick Summing
    problem

    Slick summing

    Age
    14 to 16
    Challenge level
    filled star empty star empty star

    Watch the video to see how Charlie works out the sum. Can you adapt his method?