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Secondary Live problems and recent solutions

Usually, we invite students to send us their solutions to a selection of problems, but this December and January we are doing things a little differently…

The problems below contain interactivities which offer students instant feedback, and we think they are particularly suitable to work on at home, perhaps with a family member, during the holiday period. We hope you enjoy the challenges we’ve selected.

Live problems

  • Dozens
    problem
    Favourite

    Dozens

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

    Can you select the missing digit(s) to find the largest multiple?

  • Have you got it?
    problem
    Favourite

    Have you got it?

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

    Can you explain the strategy for winning this game with any target?

  • Fruity Totals
    problem
    Favourite

    Fruity totals

    Age
    7 to 16
    Challenge level
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    In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

  • Connect Three
    problem
    Favourite

    Connect three

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

    In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

  • crossing the bridge
    problem

    Crossing the bridge

    Age
    11 to 18
    Challenge level
    filled star filled star empty star

    Four friends must cross a bridge. How can they all cross it in just 17 minutes?

Recently solved problems

  • Picturing Square Numbers
    problem
    Favourite

    Picturing square numbers

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

    Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

  • Quadratic Patterns
    problem
    Favourite

    Quadratic patterns

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

    Surprising numerical patterns can be explained using algebra and diagrams...

  • Charlie's delightful machine
    problem
    Favourite

    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?

  • m, m and m
    problem
    Favourite

    M, M and M

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

    If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

  • Slick Summing
    problem
    Favourite

    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?

  • Cyclic Quadrilaterals
    problem
    Favourite

    Cyclic quadrilaterals

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

    Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

  • Tilted Squares
    problem
    Favourite

    Tilted squares

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

    It's easy to work out the areas of most squares that we meet, but what if they were tilted?

  • Cuboid challenge
    problem
    Favourite

    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
    Favourite

    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?

  • Add to 200
    problem
    Favourite

    Add to 200

    Age
    11 to 14
    Challenge level
    filled star empty star empty star
    By selecting digits for an addition grid, what targets can you make?
  • Wipeout
    problem
    Favourite

    Wipeout

    Age
    11 to 16
    Challenge level
    filled star filled star empty star
    Can you do a little mathematical detective work to figure out which number has been wiped out?
  • Pick's Theorem
    problem
    Favourite

    Pick's theorem

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.