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In the Money

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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 24.

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 wrote:

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 2.

Jennifer from Crownfield Junior School described how she tackled the problem:

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 (1/4).

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 people:
Su who is at Kilvington Girls Grammar, Victoria, Australia said:

A quarter of the coins are heads up.
If you turn two coins over, then it would be 1/3 of the coins.
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 = 24.
The total number of coins used is 24.

Many more of you sent in correct solutions, like Thomas, but do make sure you show how you worked out the answer!