Well done, James. =D>
Concerning the Uncle and Niece:
[tab]When I read “special birthday” I just dropped it. I dislike trying to figure out what someone might think of as a “special birthday”
But later, just making guesses, I came up with a “special birthday” being 50, in which case the people could be:
7
7
50
While the Uncle is 55 and the niece 32.
I have no idea of that is the kind of thing that you were expecting.[/tab]
And then the answer to the Sudoku puzzle (in case you suspect that it can’t be done):
[tab]3 9 4 | 5 2 8 | 1 6 7
2 5 6 | 1 7 4 | 8 9 3
7 8 1 | 9 6 3 | 4 5 2
1 3 9 | 6 4 7 | 5 2 8
6 2 8 | 3 5 1 | 9 7 4
4 7 5 | 8 9 2 | 3 1 6
9 6 7 | 4 3 5 | 2 8 1
5 1 3 | 2 8 6 | 7 4 9
8 4 2 | 7 1 9 | 6 3 5[/tab]
Well done. =D>
[tab]For the age of the three persons (x, y, z):
x • y • z = 2450 = 2 • 5 • 5 • 7 • 7.
The “special birthday” is the 50th (= 2 • 5 • 5). The three persons are 50, 7, and 7 years old; the uncle is 55 years old (= 50 + 5); the niece is 32 years old (= (50 + 7 + 7) / 2).[/tab]
Your watch has stopped. So it does not work anymore. The little hand of the watch indicates approximately ten o’clock, and the big hand of the watch indicates approximately two o’clock. Both hands of the watch form an identical angle. When did your watch stop precisely?
I hate always being the only kid in the class with his hand up.
Really?
Well I got deadlines and shit. Haven’t even been able to read this thread lately.
Who is the question directed to, the wearer of the watch or somebody else who sees the watch? If the latter, it depends on how fast he is moving when he observes the watch.
Right James?
JAMES! Wake up!
Um …Huh?
yeah, right.
Whuh?
Oh …
Actually the relativistic concerns involve the fact that the minute hand is moving faster than the hour hand and the observational angle, as well as the relative speed of the observer to the appearance of simultaneity of the event.
But then again, we can assume that he asked of the actuality, not the relative appearance.
There is no problem with the text, and the task is a pure mathematical one.
So again:
Carleas!
Please come to the blackboard!
This has to be a trick question. Arminius is too smart to ask a question that is so obviously answered with “10:00 is when the clock stopped.” So, what’s the trick dude? Nobody’s playing so just give us the answer mmkay?
And what is an identical angle, anyway?
I think it is a little bit too early to give you the answer.
Both angles have the same degree. The angular degree is the same.
I don’t know what you mean by identical, but I’m not big on geometry, so I’ll explain my dumbed down misunderstanding of your statement.
If you mean each angle leaves its point of origin with the same degree relative to a line or axis drawn between them, then yeah, you have two congruent lines. But you can do this with any two angles leaving the same point of origin if you place a line directly between them.
Draw a line from the nut in the middle of the clock that bolts the hands down to the 12. There is your axis line. So each hand would have the same angle relative to the line. It would be a little more than a 45 degree angle for each hand, since the 3 and 9 would be a 90 degree angle while the 12 would be no angle.
No matter where you put the hands, you could draw a line directly between them, creating the same degree of each angle. That’s why I don’t understand what you mean when you say identical.
There is no such thing as an identical angle because all angles can be identical depending on the axis line between them.
Now if you insist that the 12 be the axis line, then putting the little hand on the 6 and the big hand on the 3, you would not have identical angles. The little hand would have a 180 degree angle while the big hand would have a 90 degree angle.
Really, mentioning that the angles are identical seems to be superfluous here.
If there are only two lines in a circle, the only two angles that can be the same is 180, that’s be either 0915 or 1445. You need another line.
Wait what? You lost me.
Draw a circle. Put a dot in the very center. Draw one line from that dot in any direction until it reaches the perimeter of the circle. Draw another one from that dot in any direction until it reaches the perimeter. Then put an axis directly in the middle between those two lines. Both of the two lines will proceed at exactly the same angle away from the axis between them.
I need a graphic. Somebody who knows what the hell I’m trying to explain here, please go find a graphic and post it.
The mathematical meaning of the adjective “identical” is identical with the mathematical meaning of the adjectives “same” and “equal”.
Please look at the watch again:
There is no doubt. The same angular degree. The two hands of the watch have the same angle. Which one it is is easily to find out.
And geometry is not enough. 
The main part of the task is not a geometrical one, by the way.
What I mean is easily to find out by the text and the picture of my post:
No.
The 12 is the axis line, but that is already clear because of the text and because of the picture. Here comes the picture again:
Geometrically “no angle” is not possible.
The equivalents betweenn the numbers of the watch and the degree values:
0 <=> 0°.
1 <=> 30°.
2 <=> 60°.
3 <=> 90°.
4 <=> 120°.
5 <=> 150°.
6 <=> 180°.
7 <=> 210°.
8 <=> 240°.
9 <=> 270°.
10 <=> 300°
11 <=> 330°.
12 <=> 360°.
Look at the watch again:
Yes, I know, but that is irrelevant. Again: What I mean is easily to find out by the text and the picture of my post:
You know from your own language that the 12 is always the pivotal point. For example: You know what it means when you say “12 o’clock”, “3 o’ clock”, or “5 past 12”, “5 past 3”, … and so on. “12 o’clock” <=> where are both hands of your watch? “5 past …” Why “5”? … You know? It is always with reference to the 12.
If the pivotal point was (it is not!) “half past 4”, then both would have identical angles (45 degrees, by the way - but according to the logic/mathematics and technique of all watches your example it is not possible, by the way). It is a tiny part of the task that one has to know what the pivotal point of a watch is.
No. It is exactly the opposite that is true.
No.
I understand everything you’ve said clearly. We are on the same page on that part. What I don’t understand is why any mention of the angle is relevant to the problem.
If the big hand is on 10 and the little hand is on 2, and the watch functions like every other watch in the known universe, and the watch has stopped working, then it stopped working at 10:10.
Now when you reveal the trick and I go ‘ohhhhhhh!’, I’m going to smack you. Now spit it out.
Graph the two angles.