In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
Use the information to work out how many gifts there are in each
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Max and Mandy put their number lines together to make a graph. How
far had each of them moved along and up from 0 to get the counter
to the place marked?
Can you replace the letters with numbers? Is there only one
solution in each case?
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Annie and Ben are playing a game with a calculator. What was
Annie's secret number?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?
Sam sets up displays of cat food in his shop in triangular stacks.
If Felix buys some, then how can Sam arrange the remaining cans in
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?
Nearly all of us have made table patterns on hundred squares, that
is 10 by 10 grids. This problem looks at the patterns on
differently sized square grids.
Sam's grandmother has an old recipe for cherry buns. She has enough
mixture to put 45 grams in each of 12 paper cake cases. What was
the weight of one egg?