My friends and I love pizza. Can you help us share these pizzas
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Katie and Will have some balloons. Will's balloon burst at exactly
the same size as Katie's at the beginning of a puff. How many puffs
had Will done before his balloon burst?
We have received loads of answers to this problem and you have
found several different ways of working it out.
Catherine and Bethany from Vernon Junior School said:
We solved this problem by trial and error. We started
with 2 heads giving a total of 8 coins. We carried on until we
tried 6 heads giving a total of 24 coins. When you turn over 2 more
heads this gives 8 heads which is a third of 24 so the answer is
Many of you used the idea that the total number of coins would
be a multiple of 3 and 4. Elizabeth explains:
As one quarter and then one third of the coins end up
as heads, the number must be a multiple of 4 and 3. 12 does not
work but 24 does.
Hussam and Suzy from Carleton St Hilda's C of E Primary School
First we thought of what number could have a quarter
and a third which are whole numbers. We came up with 12 and 24. 12
does have a third and a quarter but they have a difference of 1 so
we figured out it was 24 because 6 and 8 have a difference of
Jennifer from Crownfield Junior School described how she tackled
At first my mind was blank until I had the idea of a
method to use. I wrote out my 3 and 4 times tables. I then found
out what numbers they each share. The first number I came across
was 12 so I drew out 12 coins. I knew that 1/4 of 12 was 3 so I put
a head on 3 coins. I also knew that 1/3 of 12 is 4. This led to me
believing that I was wrong so checked my answer. I was wrong. I
then found out what other number they share in their times tables,
I of course found 24. I again drew out 24 coins and worked out 1/4
of it. I drew on 6 heads and then found out 1/3 of 24, which equals
8. I knew I was correct because 8 (1/3) was 2 less than 6
Children from Moorfield Junior School used similar ideas and
came up with the answer 24 too.
One other way of calculating the solution was described by two
Su who is at Kilvington Girls Grammar, Victoria, Australia
A quarter of the coins are heads up.
If you turn two coins over, then it would be 1/3 of the
So, a 1/3 minus a 1/4 is a 1/12.
So, 1/12 is 2 coins so 12/12 equals 24 coins.
In conclusion, there are 24 coins in total.
Oliver did it the same way. So did Dimitris and Ben from Hull.
Oliver tells us his working:
The difference between a quarter and a third is a
twelfth. Two must be a twelfth of all the coins, so there are two
times twelve coins. Twenty four is the answer.
Thomas aged 10 uses a similar idea:
Think of the whole number of coins as a pie chart. Mark
off 1/4 of it as turned on tails, then mark off 1/3 of it as how
many coins are tails after turning over two coins. You can take one
from the other (to make 30 degrees) and then divide it by two (to
make 15 degrees). If you work out how many 15 degrees go into 360
degrees you come to a final answer of 24.
Mayurun who is at Brighton College Prep School used an equation
to work out the answer:
Let a = the total amount of coins used
When 2 coins are turned over, instead of one quarter showing heads,
one third shows heads. Therefore:
a - 1/4 a = 2 so 1/12 a = 2
Times the equation by 12 to get rid of the fraction, leaving a =
The total number of coins used is 24.
a - 1/4 a = 2 so 1/12 a = 2
Many more of you sent in correct solutions, like Thomas, but do
make sure you show how you worked out the answer!