2003 AMC 10B Problems/Problem 22
Problem
A clock chimes once at 
minutes past each hour and chimes on the hour according to the hour. For example, at 
there is one chime and at noon and midnight there are twelve chimes. Starting at 
on 
on what date will the 
chime occur?
Solution
First, find how many chimes will have already happened before midnight (the beginning of the day) of 
half-hours have passed, and the number of chimes according to the hour is 
The total number of chimes is 
Every day, there will be 
half-hours and 
chimes according to the arrow, resulting in 
total chimes.
On 
the number of chimes that still need to occur is $$ (Error compiling LaTeX. Unknown error_msg)2003-91=1912.$$ (Error compiling LaTeX. Unknown error_msg)1912/180=10\text{r}112.$$ (Error compiling LaTeX. Unknown error_msg) Round up, and it is 
days past which is 
See Also
| 2003 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 21 |
Followed by Problem 23 | |
| 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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