Working systematically

problem
Ten hidden squares

Age

7 to 14

Challenge level

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
problem
Sending a parcel

Age

11 to 14

Challenge level

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
problem
Finding fifteen

Age

7 to 11

Challenge level

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
problem
Spot the card

Age

14 to 16

Challenge level

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?
problem
Nine, ten and one

Age

11 to 14

Challenge level

Can you find the value of t in these equations?
problem
Different digital clock

Age

14 to 16

Challenge level

At how many times between 10 and 11 o'clock are all six digits on a digital clock different?
problem
Square it

Age

11 to 16

Challenge level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
problem
Negative dice

Age

11 to 14

Challenge level

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?
problem
Andy's marbles

Age

7 to 11

Challenge level

Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.
problem
Orange drink

Age

7 to 11

Challenge level

A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?