February 2008
Problem of the Month
MaxMin Problem
by Sidney Kravitz
in GAMES November 2006
Each of the nine letters A through I represents a different digit from 1 through 9, but not
necessarily in that order. ABC, DEF, and GHI are three different three-digit integers.
What is the maximum possible product of these three numbers, and what is the minimum possible product?
In other words, assign different values to each letter so that ABC x DEF x GHI will be as large
as possible, and then make it as small as possible.
Solution to the Problem:
The maximum product is 611,721,516 when the letters have the following values:
| A |
B |
C |
|
D |
E |
F |
|
G |
H |
I |
|
| 9 |
4 |
1 |
x |
8 |
5 |
2 |
x |
7 |
6 |
3 |
= 611,721,516 |
The minimum product is 13,994,694 when the letters have the following values:
| A |
B |
C |
|
D |
E |
F |
|
G |
H |
I |
|
| 1 |
4 |
7 |
x |
2 |
5 |
8 |
x |
3 |
6 |
9 |
= 13,994,694 |
Correctly solved by:
|
1. K. Sengupta
|
Calcutta, INDIA
|
| 2. John Funk
|
Ventura, California
|