2003 AMC 10B Problem 22

Question

A clock chimes once at

30

minutes past each hour and chimes on the hour according to the hour. For example, at

1

PM there is one chime and at noon and midnight there are twelve chimes. Starting at

11{:}15

AM on February

26,

2003,

on what date will the

2003

rd chime occur?

March

8

March

9

March

10

March

20

March

21

In each

12

-hour period there are

12

half-hour chimes and

1+2+\cdots+12=78

hour chimes

A full day has

180

chimes; count how many occur after

11{:}15

AM on Feb

26

and accumulate by day

Each

12

-hour period has

12 + 78 = 90

chimes, so each full day has

180.

After

11{:}15

AM on February

26,

the rest of that day has

91

chimes. Adding

180

for each following full day, the count reaches

1891

by the end of March

8.

The remaining chimes fall on March

9:

the

2003

rd chime is the

112

th chime of that day, occurring at

3{:}30

PM on March

9.

Thus, the correct answer is B.

Problem 22 in other years