What number is it that, when multiplied by 18, 27, 36, 45, 
54, 63, 72, 81, or 99, gives a product in which the first 
and last figures are the same as those in the multiplier, 
but which when multiplied by 90 gives a product in which 
the last two figures are the same as those in the multiplier?
 
 
 
 

                  THE SOLUTION
 

The number is 987,654,321, which, when multiplied by 18,
gives 17,777,777,778, with 1 and 8 at the beginning and
end. And so on with the other multipliers, except go,
where the product is 88,888,888,890, with 90 at the end.
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