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Forgot the Numbers

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

We had nearly $100$ solutions sent in for this challenge.

We also had one sent in to the blog.  Here are just some of them.

From Forest Lake State School in Australia we had contributions from $3$ pupils, Long, Daniel and this is Connor's":


At first I did this:

$46$ divided by $15=3.0666666$
$44$ divided by $14=3.1428571$
$43$ divided by $14=3.0714285$
$42$ divided by $14=3$
$41$ divided by $14=3.1538461$
$39$ divided by $13=3.25$
$38$ divided by $12=3.1666666$v
$36$ divided by $12=3$
$29$ divided by $12=3.2222222$
$28$ divided by $9=3.1111111$
$27$ divided by $9=3$
$26$ divided by $9=3.25$
$25$ divided by $8=3.125$

The last division sum is the correct answer. At first I did $46$ sided by
$15=3.06666666$, so I knew the two numbers had to be lower. When I got down
to $25$, I knew that the dividing number had to be reasonable. So I tried 8.
Hey presto! I got the answer right. Last algorithm - $25$ divided by $8= 3.125$.


Isabella from Sharp school, together with Mellisa and Rebecca had a different way of approaching it:

Firstly I wrote down the 3.125 times table:
$3.125, 6.25, 9.375, 12.5, 15.625, 18.75, 21.875, 25, 28.125, 31.25$
I saw the only whole number was $25$ ($8$ lots of $3.125$) so that means $25$
divided by $8$ is $3.125$.


A number of different approaches were shown by pupils from Rykneld School in the UK. The pupils were, Alice, David, Jordan, Kieran, Daniel, Alicia and Alice who suggested a further challenge:


After we had worked out the solution to the problem, we made our own!

I divided two numbers and got the answer of $13.5$.  I can't remember my two
numbers but they are both under $75$ and are whole numbers.  Can you work out
what my numbers were?


From Huy at the Australian International School of Vietnam we had the following:

We call these two numbers as X and Y.
I know that $3.125$ equals to fraction $3 1/8$.

$X = (3 1/8)$ times Y and Y is the whole number -->   Y must be a multiple of $8$.

Because X and Y are under $50$, I figure out $Y = 8, X = 25$


From Varsity Acres in Canada we had the following message, ( they sent in a pictures of their work but unfortunately we were not able to use it.)

Student work, done in French , a student discovered the connection between $0.125$ and $125$.

$8$ x $125 = 1000$ so - $1.0$!$ A fantastic leap and she brought the class along.


Well done all of you. I'm sorry we cannot publish all the solutions!