This is a game for two players. You will need some small-square
grid paper, a die and two felt-tip pens or highlighters. Players
take turns to roll the die, then move that number of squares in a
straight line. Move only vertically (up/down) or horizontally
(across), never diagonally. You can cross over the other player's
trails. You can trace over the top of the other player's trails.
You can cross over a single trail of your own, but can never cross
a pair of your trails (side-by-side) or trace over your own trail.
To win, you must roll the exact number needed to finish in the
target square. You can never pass through the target square. The
game ends when a player ends his/her trail in the target square, OR
when a player cannot move without breaking any of the rules.
Identical discs are flipped in the air. You win if all of the faces
show the same colour. Can you calculate the probability of winning
with n discs?
What Does Random Look Like?
Age 11 to 14 Challenge Level:
On a strip like the one below, ask a friend to make up a sequence
of twenty Hs and Ts that could represent a sequence of heads and
tails generated by a fair coin, and ask them to write "made
up" lightly in pencil on the back of the strip.
Then ask your friend to flip a fair coin twenty times and
record the results on a second strip, and this time ask them to
write "real" lightly in pencil on the back.
Take the two strips and try to work out which was real and which
was made up - you could create similar strips and challenge your
friend in the same way.
Here is an animation which generates twenty random coin flips.
Hover over the bars on the bar chart to see how the runs have been
Use the animation to generate several sequences of twenty coin
flips, and try to get a feel for the features you would expect a
random sequence to have.
How would you analyse whether a sequence came from a real
Send us your ideas and justify the method you use to decide.
Are you now better at spotting fakes? Ask your friend to
create two more strips and see if you can find the truly random
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.