![The Third Dimension](/sites/default/files/styles/medium/public/thumbnails/content-02-12-penta5-icon.gif?itok=GjGzITlu)
problem
The Third Dimension
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
![Consecutive Numbers](/sites/default/files/styles/medium/public/thumbnails/content-97-11-bbprob2-icon.jpg?itok=C_UREbsv)
problem
Consecutive Numbers
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
![Buying a Balloon](/sites/default/files/styles/medium/public/thumbnails/content-01-01-letme1-icon.png?itok=4_BYOktc)
problem
Buying a Balloon
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
![How many Times?](/sites/default/files/styles/medium/public/thumbnails/content-00-01-penta3-icon.jpg?itok=0F_QWl3d)
problem
How many Times?
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
![Square Corners](/sites/default/files/styles/medium/public/thumbnails/content-02-11-penta4-icon.gif?itok=9M-qCvJY)
problem
Square Corners
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
![A Square of Numbers](/sites/default/files/styles/medium/public/thumbnails/content-03-11-penta2-icon.gif?itok=wlJ1dBta)
problem
A Square of Numbers
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
![A Mixed-up Clock](/sites/default/files/styles/medium/public/thumbnails/content-02-07-penta2-icon.gif?itok=XVrNlnIx)
problem
A Mixed-up Clock
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
![Magic Vs](/sites/default/files/styles/medium/public/thumbnails/content-id-6274-icon.png?itok=dRZNbkAI)
problem
Magic Vs
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
![Fifteen cards](/sites/default/files/styles/medium/public/thumbnails/content-id-7506-icon.png?itok=z3XnnkJh)
![Take three numbers](/sites/default/files/styles/medium/public/thumbnails/content-id-8063-icon.png?itok=xAzr90zq)
problem
Take three numbers
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
![Play to 37](/sites/default/files/styles/medium/public/thumbnails/content-id-10328-icon.gif?itok=h40d-8u2)
problem
Play to 37
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
![Build it up](/sites/default/files/styles/medium/public/thumbnails/content-id-10592-icon.png?itok=QjqjP4l_)
problem
Build it up
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
![Roll these Dice](/sites/default/files/styles/medium/public/thumbnails/content-98-10-bbprob2-icon.png?itok=cj85bw5d)
problem
Roll these Dice
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?
![Wonky Watches](/sites/default/files/styles/medium/public/thumbnails/content-00-05-penta4-icon.jpg?itok=JgEjEJ81)
problem
Wonky Watches
Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.
![Amy's Dominoes](/sites/default/files/styles/medium/public/thumbnails/content-01-03-penta1-icon.png?itok=yIgH25d0)
problem
Amy's Dominoes
Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?
![Sealed Solution](/sites/default/files/styles/medium/public/thumbnails/content-03-06-penta4-icon.gif?itok=doeBT_KV)
problem
Sealed Solution
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
![Got It](/sites/default/files/styles/medium/public/thumbnails/content-02-01-game1-icon.png?itok=YpX97D5X)
problem
Got It
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
![Finding Fifteen](/sites/default/files/styles/medium/public/thumbnails/content-id-2645-icon.png?itok=dCkzVLdA)
problem
Finding Fifteen
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?
![Oh! Harry!](/sites/default/files/styles/medium/public/thumbnails/content-id-5979-icon.png?itok=AAhYlqkp)
problem
Oh! Harry!
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
![This Pied Piper of Hamelin](/sites/default/files/styles/medium/public/thumbnails/content-id-8315-icon.gif?itok=BPa6O2ul)
problem
This Pied Piper of Hamelin
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
![Watch the clock](/sites/default/files/styles/medium/public/thumbnails/content-00-01-penta2-icon.jpg?itok=dg4uLtYD)
problem
Watch the clock
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
![5 on the clock](/sites/default/files/styles/medium/public/thumbnails/content-98-10-penta1-icon.gif?itok=pvYbgg49)
problem
5 on the clock
On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
![Inky Cube](/sites/default/files/styles/medium/public/thumbnails/content-id-7241-icon.jpg?itok=RLwPEkH8)
problem
Inky Cube
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
![Dice in a Corner](/sites/default/files/styles/medium/public/thumbnails/content-id-8586-icon.png?itok=afailiuC)
problem
Dice in a Corner
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?