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
60h+m=(1/4)*(60(h-12)+m)+(1/2)*(60*12+60(23-h)+60-m)
expanding and collecting we get
60h+m=900-15h-(m/4)
75h+(3m/4)=900
300h+3m=3600
100h+m=1200
100h=1200-m
since 0<=m<60
then 1140<1200-m<=1200
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