MrRubix's Riddle Thread

[hoochan]

Originally Posted by MrRubix_MK5

In this thread, we will dedicate discussion to various riddles/puzzles/problems.

Here's one to get you started.

Imagine that the hour and minute hands of a clock are the same length. Imagine, also, that I am able to read the hands with 100% certainty (meaning I can tell EXACTLY how far the hour/minute hands have moved).

How many times exist over a 12 hour period where, if I were to look at the clock, I'd be unable to tell you what time it was?

ohhhh i missed that the first time

[s0ulst0n3]

You will always know the time because the minute hand goes faster then the hour hand. If you are watching it for a 12 hour span of time, then you will know the time easily.

Unless it is unplugged/broken, then you won't be able to tell the time, lol.

[MrRubix_MK5]

Some really basic help: When the minute hand goes 360 degrees, the hour hand goes 30 degrees (360/12).

[MahouMinachan]

I thought using Matrices would help, but all it did was make me more confused...

[sc979]

You really should edit the first post to say that the answer is NOT '11', '12', 'you'll always be able to tell', or 'you'll never be able to tell' so that people will stop guessing them.

[MrRubix_MK5]

Come on guys, you can do it :P

[emerald000]

Haven't really thought about it, but I would say an infinity of times. The only ones you WOULD be able to determine are when both hands are together. For the others, it is always impossible to determine which is which.

PS: I am pretty sure I miss something, since this is too obvious...

[s0ulst0n3]

Originally Posted by MrRubix_MK5

Come on guys, you can do it :P

how many degrees does the minute hand move after the second hand makes a complete 360?

[MrRubix_MK5]

There is a minute hand and an hour hand. No second hand, here.

Since a new hour begins every 60 minutes, the minute hand travels 360 degrees per hour while the hour hand travels 30 degrees per hour. So when the minute hand moves x degrees, the hour hand is moving x/12 degrees.

emerald: if both hands are overlapping perfectly, would you be able to tell me which hand was the hour and minute hand? When would you be unable to tell?

[humphoboextreme]

Wouldn't it be slightly before and slightly after the minute hand crosses the hour hand that makes it impossible to tell? which means out of 12 times x 2 makes 24 times for each hour? If you're asking for the time, I'm too lazy... if I'm wrong, then I have no idea.

[emerald000]

I couldn't, but who cares? You could easily tell the time. If they are both on the 12, you know it is 12:00. If they are both a little past one, you know it is 1:0x (don't feel calculating).

And after more thinking, I realized you can tell some other hours if the hour hand isn't exactly the good distance of the number. But that is still an infinity of possibilities.

[Dr McGoodTimes]

A quick question: Does the minute hand move as though there was a second hand? What I mean is, since the minute hand moves 6 degrees every sixty seconds, does it move 6 degrees every minute on the minute, or does it 1/10 of a degree every second?

[MrRubix_MK5]

Originally Posted by Dr McGoodTimes

A quick question: Does the minute hand move as though there was a second hand? What I mean is, since the minute hand moves 6 degrees every sixty seconds, does it move 6 degrees every minute on the minute, or does it 1/10 of a degree every second?

All movement is continuous. The hands don't "spring" from one time to another. They flow smoothly over the entire range.

[rushyrulz]

You can't tell us 24 times? If its right and I need to show you math, I will. (Even tho its probably way wrong.)

[Dr McGoodTimes]

I'm just gonna jot down some (possibly useless) notes.

The hour hand moves at 1/12th the speed of the minute hand.

The minute hand moves 1/10th of a degree per second. Thus, the minute hand has 3600 different positions on the clock (1/10th degree, 1/5 degree... all the way to 360 degrees).

Since the hour hand moves at 1/12 the speed, it moves 1/120th of a degree a second, and has 43200 positions on the clock.

Dunno how useful this is.

[humphoboextreme]

Originally Posted by rushyrulz

You can't tell us 24 times? If its right and I need to show you math, I will. (Even tho its probably way wrong.)

Well, this thing doesn't make sense. I don't need much math for my solution.


What we're looking at is something visual. Math doesn't need to be there to prove it.

If the minute hand is right next to the hour hand, the colors of the hands may blend into one. When that happens, you can't tell where each one is, and when it is one minute past, it will look the same, right? I'm not completely sure, if you're looking at it non-stop, then there's 0% chance you'll never know the time.

[MrRubix_MK5]

Dr McGoodTimes: There are infinitely many "positions" -- as I said in my response to your question, the movement is continuous. The minute hand could be located at 54.435843508435904 degrees for all it matters. It goes across the entire range at a constant rate.



EDIT because of humpyhobopersonXTREEMELolz: Ok if you answer anything that has been answered in some form on this thread already, I just won't respond to it.

No times = wrong
All times = wrong

[MahouMinachan]

I've got to ask, how far of a Math background do we need to solve this?

[MrRubix_MK5]

Nothing fancy. If you understand the problem and what you would have to do to solve it, then you likely know enough math to figure out the solution.

[PuRoDoMiNiCaNo]

How many times exist over a 12 hour period where, if I were to look at the clock, I'd be unable to tell you what time it was?

So the answer would be however many times the hands overlap right? If so, just take a watch and turn the dial and count how many times it overlaps until you 12 noting the time that the hands overlapped