QUEER MULTIPLICATION

If I multiply `51,249,876` by `3` (thus using all the nine digits once, and once only), I get `153,749,628` (which again contains all the nine digits once). Similarly, if I multiply `16,583,742` by `9` the result is `149,253,678`, where in each case all the nine digits are used. Now, take `6` as your multiplier and try to arrange the remaining eight digits so as to produce by multiplication a number containing all nine once, and once only. You will find it far from easy, but it can be done.