Difference between revisions of "1990 AJHSME Problems/Problem 1"
5849206328x (talk | contribs) (Created page with '==Problem== What is the smallest sum of two <math>3</math>-digit numbers that can be obtained by placing each of the six digits <math>4,5,6,7,8,9</math> in one of the six boxes …') |
(→Solution) |
||
(3 intermediate revisions by 2 users not shown) | |||
Line 24: | Line 24: | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
+ | {{MAA Notice}} |
Latest revision as of 16:12, 29 October 2016
Problem
What is the smallest sum of two -digit numbers that can be obtained by placing each of the six digits in one of the six boxes in this addition problem?
Solution
Let the two three-digit numbers be and . Their sum is equal to .
To minimize this, we need to minimize the contribution of the factor, so we let and . Similarly, we let , , and then and . The sum is
See Also
1990 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.