Use all the digits 1 to 9 create three 3-digit numbers, which, when multiplied together creates the highest value possible.

firstly some lay man's explanation.
When multiplying 2 number together to get the highest value, the 2 numbers need to be as close as possible.

e.g. any 2 numbers totalling 10.
1*10=10,
2*9=18,
3*7=21,
4*6=24,
5*5=25,
6*4=24. etc. etc.

using the same theory for this puzzle, and also maintaining that each three digit number must be as large as possible,
we get 9, 8 & 7 as the hundreds digits,(H)
and 6, 5 & 4 as the tens digits,(T)
with 3, 2 & 1 as the units digits.(U)

from this we need the highest number to be 941 (highest H, lowest T & U)
and the lowest number to be 763 (lowest H, highest T & U)
this leaves 852 as the middle number.

the sum being 941*852*763=611,721,516

Posted by Juggler on 2004-09-18 13:43:33