Difference between revisions of "2006 AMC 12A Problems/Problem 4"
m (→Solution 2) |
m (→Solution 2) |
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With a matrix we can see | With a matrix we can see | ||
<math> | <math> | ||
| − | + | \begin{bmatrix} | |
1+2&9&6&3\\ | 1+2&9&6&3\\ | ||
1+11&8&5&2\\ | 1+11&8&5&2\\ | ||
1+0&7&4&2 | 1+0&7&4&2 | ||
| − | \end{bmatrix} | + | \end{bmatrix} |
</math> | </math> | ||
The largest digit sum we can see is <math>9</math> | The largest digit sum we can see is <math>9</math> | ||
Revision as of 17:58, 23 July 2018
- The following problem is from both the 2006 AMC 12A #4 and 2008 AMC 10A #4, so both problems redirect to this page.
Contents
Problem
A digital watch displays hours and minutes with AM and PM. What is the largest possible sum of the digits in the display?
Solution 1
From the greedy algorithm, we have 
in the hours section and 
in the minutes section. 
Solution 2
With a matrix we can see
The largest digit sum we can see is
For the minutes digits, we can combine the largest 
digits, which are 
which we can then do 
See also
| 2006 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 3 |
Followed by Problem 5 |
| 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 12 Problems and Solutions | |
| 2006 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
