[ March 26, 2001 ]
A Ninedigital Divertimento
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 webpages
for more 'Ninedigital diversions' !

[ The complete 39-list is accessible at
The Nine Digits Page 6. ]