Exploring and noticing

  • Last Biscuit
    game

    Last biscuit

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

    Can you find a strategy that ensures you get to take the last biscuit in this game?

  • How old am I?
    problem
    Favourite

    How old am I?

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

    In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

  • Pair Products
    problem
    Favourite

    Pair products

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

    Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

  • Warmsnug Double Glazing
    problem
    Favourite

    Warmsnug double glazing

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

    How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

  • Where is the dot?
    problem
    Favourite

    Where is the dot?

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

    A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

  • Power Countdown
    problem
    Favourite

    Power countdown

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

    In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

  • A little light thinking
    problem
    Favourite

    A little light thinking

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

    Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

  • Last one standing
    problem
    Favourite

    Last one standing

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

    Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

  • Generating Triples
    problem
    Favourite

    Generating triples

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

    Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

  • Electric Kettle
    problem

    Electric kettle

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

    Explore the relationship between resistance and temperature