A: "The time now equals quarter of the time that passed since noon till now plus half of the time left from now till tomorrow's noon."
Please express R's response in HH:MM format.
Abridged from Dudeney's " Amusements in Mathematics" (1917)
assuming HH:MM is in 24hr format
let h be the hours and m be the minutes
then the time in minutes since 00:00 is 60h+m
minutes since noon, 60(h-12)+m
minutes until noon next day, 60*12+60(23-h)+60-m
thus we have
expanding and collecting we get
the only multiple of 100 in this interval is 1200
thus 1200-m=1200 gives m=0 and h=12
thus the time is noon :-D
Posted by Daniel
on 2011-09-19 14:48:58