Math Puzzle: Faulty Clock

Assuming that the rotary arm is geared to a one minute rotation the clock will gain "one second" every minute.

Q1 ordinary year=365x24x60mins
->Clock gains 365x24 mins= 6.08333...days
Time reads 12+2.00=14.00

Q2 leap year=366x24x60 mins
->Clock gains 366x24 mins=6.1 days
Time reads 12+ 2.4 hours =14.24

Actually, I'm now thinking it loses a second per minute (one second per stroke)....in which case the two answers are 10.00 and 09.36 respectively.

Hint:

The general structure of any clock is that all 3 arms SHARE the central rotating rod.

So the defect (add or loss) is common in all arms i.e. seconds, minute & Hour each as they all lie on the same defective rotatory motor. Only thing is each structs with different momentum being on different sized disks.

I get:
12:23:36.39
and
12:00:00

Mark How do you reach a decimal in seconds... ? We normalize the puzzle in the lowest unit of time, that is seconds. So ultimate time must always be in whole seconds.

Because most of the time, N * (60/61) is not a whole number.

this is how I see it..........

For every minute you lose one second
For every hour you lose 60 seconds and one minute
For every day you lose 1440 seconds, 24 minutes and 1 hour

This totals 108 minutes/day
X 365 days=38340 minutes lost for the year

Divided by 60 (for total hours lost for the year)= 639 hours lost in the year

639-624(26 days x 24 hours) (take off all of those whole days, because days don't matter on a standard clock) which leaves you with 15 hours..........

take off those additional 12 which leaves you 3 hours behind so 9 o'clock

my head hurt so I didn't figure out the leap year portion, but I assume it would be pretty easy using the 108 minutes per day loss.

acedogg is correct!

I disagree. A second is not lost every minute. A second is lost every 61 seconds.

There are math freaks and then there is markr.

He is correct (as usual).

If the normal clock is at the 60 second mark the faulty clock would still be one second away from being at one minute, hence you lose 1 second every time this happens. If the normal clock is at the 120 second mark the faulty clock would now be 2 seconds away from being at the 120 second mark and so on.

If the faulty clock takes 61 "ticks" to complete a revolution, then the faulty clock will be at 60 seconds when the normal clock is at 61 seconds. You lose one second every 61 seconds.

I agree, but I believe that you would use this reasoning if the question was: "The faulty clock reads 1200 at the end of a year what time did the normal operating clock read?" We are using the given, which is standard time (the wrist watch) so we have to figure out what happens during a given minute and at the end of 60 seconds the faulty clock would be one second (one tick) behind because it takes 61 seconds to get around one revolution. Either way? You explanation is true, I can't argue that, but somehow I did get the correct answer?

After 60 seconds, you've lost 60/61 of a second. I don't think your answer is correct.

well if each stroke is 60/61 seconds....then wouldn't it not matter and the time would be the same?

I interpreted the statement to mean that a stroke occurs every second, but it takes 61 strokes to make a complete revolution. After 60 seconds, 60/61 of a revolution has been made.

Okay, I have been thinking about this and this is what I have come up with.........

I asked myself where would the faulty clock be at 60 seconds? The correct answer is it would be at 60 seconds, it is still ticking one click per second like the other clock it just has a longer "complete rotation", so it would be one second short of its own full circle. Now at 120 seconds the faulty clock would be at 120 seconds but it would be 2 seconds away from reaching its goal of two whole rotations because it actually needs to get to 122 to complete two rotations. And so on............Does this make sense or am I obsessing?

At the end of one hour the goal for the normal clock would be 60 seconds x 60 minutes=3600 seconds. and the faulty clocks final goal for the hour would be 61 secondsx60 minutes=3660, but it would still be at 3600, hence losing 60 seconds.