Use all the digits 1 to 9 create three 3digit 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 20040918 13:43:33 