Q) a digit number, when multiplied by reverses its digits. for example becomes . find the number.


my (very long) solution :
let the number be

then we have

it is simple to notice that since divides the left hand side, must be even. but is the first digit of a digit number which when multiplied by gives another digit number. hence .
note that this holds since the number we want must be .

plugging this value of in , we get -

so this means that is
.
so may be or .
clearly is the first digit of number greater than , so must be .

now we have

now since is divisible by ,
and , we must have .
by some hit and trial at


so the number is .