Exploring and noticing

  • Four Coloured Lights
    problem

    Four Coloured Lights

    Age
    11 to 14
    Challenge level
    Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?
  • Take a Leaf
    problem

    Take a Leaf

    Age
    11 to 14
    Challenge level

    An examination paper is made from five pieces of paper. What is the sum of the other page numbers that appear on the same sheet as page 5?

  • Small tomato seedlings in pink pots.
    problem

    Halloween Day

    Age
    11 to 14
    Challenge level

    One year there were exactly four Tuesdays and four Fridays in October. On what day of the week was Halloween.

  • Small pepper seedlings in orange pots.
    problem

    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?

  • Pair Sums
    problem

    Pair Sums

    Age
    11 to 14
    Challenge level

    Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

  • Hallway Borders
    problem

    Hallway Borders

    Age
    11 to 14
    Challenge level

    What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?

  • One to Eight
    problem

    One to Eight

    Age
    11 to 14
    Challenge level

    Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

  • Top-Heavy Pyramids
    problem

    Top-Heavy Pyramids

    Age
    11 to 14
    Challenge level

    Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

  • Small tomato seedlings in pink pots.
    problem

    Too Close to Call

    Age
    11 to 14
    Challenge level

    Weekly Problem 24 - 2012
    Can you put these very close fractions into order?

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