Difference between revisions of "1989 AJHSME Problems/Problem 14"
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When placing each of the digits <math>2,4,5,6,9</math> in exactly one of the boxes of this [[subtraction]] problem, what is the smallest [[difference]] that is possible? | When placing each of the digits <math>2,4,5,6,9</math> in exactly one of the boxes of this [[subtraction]] problem, what is the smallest [[difference]] that is possible? | ||
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<cmath>\begin{tabular}[t]{cccc} | <cmath>\begin{tabular}[t]{cccc} | ||
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- & & \boxed{} & \boxed{} \\ \hline | - & & \boxed{} & \boxed{} \\ \hline | ||
\end{tabular}</cmath> | \end{tabular}</cmath> | ||
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| + | <math>\text{(A)}\ 58 \qquad \text{(B)}\ 123 \qquad \text{(C)}\ 149 \qquad \text{(D)}\ 171 \qquad \text{(E)}\ 176</math> | ||
==Solution== | ==Solution== | ||
Latest revision as of 10:49, 30 July 2023
Problem
When placing each of the digits 
in exactly one of the boxes of this subtraction problem, what is the smallest difference that is possible?
![\[\begin{tabular}[t]{cccc} & \boxed{} & \boxed{} & \boxed{} \\ - & & \boxed{} & \boxed{} \\ \hline \end{tabular}\]](http://latex.artofproblemsolving.com/0/b/9/0b9dc6ca66d1221bfd87eb8a6acf4dc728f13d89.png)
Solution
When trying to minimize 
, we minimize 
and maximize 
. Since in this problem, is three digit and is two digit, we set 
and 
. Their difference is 
.
See Also
| 1989 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 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. 
