<PRE><B>Question 472129</B>
I will start the day at 1 AM
The clock chimes {{{ 2*1 = 2 }}} times
The number of on  the hour chimes are:
{{{ 2*1 + 2*2 + 2*3 + 2*4 }}} . . . to {{{ 2*24 }}}
{{{ 2*( 1 + 2 + 3 + 4 ) }}} etc.
The formula for the sum of digits 1 through n is
{{{ (1/2)*n* (n+1) }}}
When {{{ n = 24 }}}
Twice the sum = {{{ 2*(1/2)*24*25 }}}
{{{ 24*25 = 600 }}}
3 chimes each half hour, from 1:30 AM to 11:30 PM is {{{ 23 }}} chimes
{{{ 23*3 = 69 }}}
Total = {{{ 600 + 69 = 669 }}} answer
Hope I got it</PRE>