Easy question
...but worth thinking about how you can get the answer quickly. And how many different answers there are.
This comes from brilliant.org
This comes from brilliant.org
Work out x
How did you do it?
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Simple to simplify?
This is a lovely question that I was emailed by brilliant.org If you haven't seen that site then do go there. I suggest signing up for the free access and having fun exploring some of their frankly brilliant problems. This one involves some nice techniques and will allow you to delve into different A-level maths ideas.
There are 16 possible solutions:
ReplyDeleteAssuming
a x b = c
I + j = k
x - y = z
You start of by finding that c can only equal 6 or 8 meaning a or b must equal 2.
Since you can also conclude that either k or x must equal 9 you can arrive with 12 different equations.
When k or x = 9
1,8
3,6
4,5
5,4
6,3
8,1
We will ignore the last there as they are just the other way around.
We can find out that there is no way to use 1,8 or 3,6 but is a way for 4,5.
We also know that a can switch with b, I can switch with j and y can switch with z. This gives 8 possible rearrangements.
Since x or k could equal 9 there is double 8 amount of solutions making it 16.