A Ninedigital Divertimento.

[ *March 26, 2001* ] by Janean Wilson (email)

Janean Wilson from Grand Rapids, Michigan wanted to know the highest possible

product of three 3-digit numbers, *all nine of whose digits are different*.

One can differentiate two cases.

First the three 3-digits numbers can be anything.

My program gave quite a lot of solutions (**59996** in fact)

The largest solution is the 'one but last' from my output

list (coincidentally palindrome **59995**)

972 * 997 * 998 = 967145832

The second case is when an extra condition is imposed on the

expansion of the three multipliers namely that they must also be

ninedigital. Only **39** of the above **59996** fulfil this condition and

the largest one is this beautiful

531 * 876 * 942 = 438176952

Note **39** standing for **3** multipliers and **9** digits !

I recommend the interested reader my webpage

for more ninedigital diversions !