Maths question-number cards

[Mumstheword]

Hi all
Wondered if anyone could help with the question on a past paper with 5 number cards and you need to complete a calculation

1 4 5 7 9

Use all 5 cards to complete the calculation

___ ____ _____ - _____ ______ = 654

Is there a short cut to work these out or is it just trial and error?

Thanks for any help!

[parent2013]

Hit n trial but the hint lies in number 54 which can be obtained by subtracting
9-5=4
9-4=5

7 9 9
1 4 5
----------
6 5 4
----------

[southbucks3]

Hit n trial but the hint lies in number 54 which can be obtained by subtracting
9-5=4
9-4=5

7 9 9
1 4 5
----------
6 5 4
----------

There are only 5 numbers!

You know you are reducing the first number by less than 100 because there is only two gaps after the minus and it has to be more than 600, so hundreds column can only be 7. Then start at units...what makes 4? 9-5 or 5-1, then look at tens, what makes 5 (1)4-9 or 9-4

So by process and a bit of trial and improvement 745 -91 =654

Edited...due to gumbiness

[parent2013]

So by process 795-41 =654

Check your process again

[southbucks3]

Ok so what's a hundred between friends

We are both pants! Good job we are not ten

Same theory, but 745 -91 =654 . Which is what I had written on a til receipt, but obviously lost my brain on the iPad!

[nyr]

I think the following approach may be worth mentioning as it avoids trail and error.

Let ab denote the 2 digit number and cde denote the 3 digit number and let us start by adding 654 to ab.

654
+ ab
-----
cde

There is a carry of 1 into hundreds which implies c=7.
5+b leads to a carry and 5+b is not = 10 which implies a=9
5+9=10+d which implies d=4
no carry from units column which implies b=1 and e = 5

ab is 91 and cde is 745

DS in Y6 went for the trial and error approach, though this was at 9:15PM and after 1.5 hours of swimming squad training!

nyr

[Sutty961]

Very complicated method