Est. 1998 — 27 years of woodworking knowledge
Friday Puzzler Bonus -- what time
Alex Y
When looking for a puzzler for this week, I looked at the wall clock and noticed that at that time, if you added one quarter of the time from noon yesterday to one half of the time until noon today, the result would be the time. What time was it?
Re: Friday Puzzler Bonus -- what time
Larry Barrett
The sum of the digits in the answer (hh:mm) is 10.
Re: Friday Puzzler Bonus -- what time
Alex Y
Not in the result I am aware of, and I think the answer is unique. Post your solution.
Re: Friday Puzzler Bonus -- what time
Larry Barrett
I made an error in arithmetic in my answer (sum of digits = 10). Should be sum of digits = 13. Solution below.
Let T be the time we are looking for, as measured from 00:00 today. From the problem statement, T is sometime between 00:00 and 12:00 today.
So T = (1/4) x (the time from noon yesterday) + (1/2) x (the time until noon today).
T = (1/4)(12+T) + (1/2)(12-T)
T = 3 +(1/4)T + 6 - (1/2)T
T = 9 - (1/4)T
(5/4)T = 9
T = 36/5
T = 7.2 = 07:24
Stick to your guns! Nice job
Alex Y
In fact, your initial answer was right. last step, 7.2-7:12, not 7:24, so the sum of digits is 10, as you originally stated. And your answer is the only correct answer (I believe) when using a 24-hour designation of time.
The answer I had was based on the ambiguity of the 12-hour clock:
At 9:36 last night, the time was equal to 1/4 of time after yesterday noon (9.6 / 4 = 2.4) plus 1/2 of the time until today noon (14.4 / 2 = 7.2) = 9.6.