Find the smallest number that is made up of each of the digits $1$ through $8$ exactly once and is divisible by $88$.
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Looks like this is a modified version of the problem at MathsChallenge (on page 29) You should go read that and try solving yourself.
If someone else comes with a different approach, that probably will be helpful to you.
You should also mention what was your approach (You would have started somewhere, didn't you?)
It's been a long day for me so far but if the number is divisible by $88$ shouldn't it therefore be divisible by $11$? If that's the case shouldn't the last two digits be $\ldots 21$?