Difference between revisions of "2022 AMC 10A Problems/Problem 17"
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==Solution== | ==Solution== | ||
| + | Notice that <math>0.\overline{abc} = \frac{abc}{999} </math>and <math>0.\overline{x} = \frac{x}{9}</math>. From this, we can write: | ||
| − | ~ | + | |
| + | Solution in progress | ||
| + | |||
| + | ~KingRavi | ||
== See Also == | == See Also == | ||
Revision as of 02:21, 12 November 2022
Problem
How many three-digit positive integers 
are there whose nonzero digits 
and 
satisfy
![\[0.\overline{\underline{a}~\underline{b}~\underline{c}} = \frac{1}{3} (0.\overline{a} + 0.\overline{b} + 0.\overline{c})?\]](http://latex.artofproblemsolving.com/9/e/4/9e448c87f48492e9f1518a6989dee06242cab99f.png)
(The bar indicates repetition, thus 
in the infinite repeating decimal 
Solution
Notice that 
and 
. From this, we can write:
Solution in progress
~KingRavi
See Also
| 2022 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 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 AMC 10 Problems and Solutions | ||
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