I've never used a telescope.
I once had a Canon TTL camera with a 75-210 zoom and a 3x televerter that gave me 630x, and I set it up on a tripod to view a comet's tail. However, it was too cloudy and I saw nothing...and I froze.
I should have tried again, but haven't really had the interest and now I don't have that camera anymore.
Off to bed now...catch you later.
I have a Sony camera with a little telescopic lens, and an imagination that fills in any missing information that my camera may not have picked up for one reason or another.
I don't know how good the viewing is from here. All I know is that viewing the heavens is best done at night, but that's when I'm either asleep in bed or asleep at my computer, so I don't get to see much then.
I was just reading up on him...
Later, with notable thanks to the observations of the Italian astronomer Vincenzo Cerulli, scientists came to the conclusion that the famous channels were actually mere optical illusions. The last popular speculations about canals were finally put to rest during the spaceflight era beginning in the 1960s, when visiting spacecraft such as Mariner 4 photographed the surface with much higher resolution than Earth-based telescopes, confirming that there are no structures resembling "canals".
Or had all the water run out of the canals and dropped off the planet, and all evidence of their existence eroded away, by the time Mariner 4 came along...?
Here are two options that, by making one change to the puzzle in post #6, converts it from unsolvable to one that has a unique solution:
Option 1: C1 empty Option 2: G1 empty 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 A | _ 2 _ | 1 5 _ | _ _ _ | A | _ 2 _ | 1 5 _ | _ _ _ | B | _ _ 5 | 2 _ _ | _ _ 9 | B | _ _ 5 | 2 _ _ | _ _ 9 | C | _ _ _ | _ _ 4 | _ 2 5 | C | 3 _ _ | _ _ 4 | _ 2 5 | |-------+-------+-------| |-------+-------+-------| D | _ 8 7 | _ _ 2 | 5 _ _ | D | _ 8 7 | _ _ 2 | 5 _ _ | E | _ 4 _ | _ 1 7 | _ _ _ | E | _ 4 _ | _ 1 7 | _ _ _ | F | _ _ _ | _ _ 3 | 1 _ 7 | F | _ _ _ | _ _ 3 | 1 _ 7 | |-------+-------+-------| |-------+-------+-------| G | 2 _ 4 | 6 _ _ | _ _ _ | G | _ _ 4 | 6 _ _ | _ _ _ | H | 6 _ _ | _ 9 _ | _ 3 _ | H | 6 _ _ | _ 9 _ | _ 3 _ | I | _ 5 _ | _ _ _ | 9 6 8 | I | _ 5 _ | _ _ _ | 9 6 8 |
Both solutions are easy to find, and are different from each other.
Hi, Leren (Dutch for 'learn'), and welcome to the forum!
Well, that's interesting information! I'd suspected that there would be many more solutions to the OP's puzzle (post #1) than the few that I'd found with the Excel Solver add-in I referred to in other posts, but not as many as that!!!
How did you arrive at that total, and what program did you use?
The hour and minute hands are at equal distance from the 6 hour, what time will it be exactly?
There are 12 solutions where the two hands are on different sides of the clock face, and the distance to the 6-hour mark for one is measured in the reverse direction to that of the other.
There are 11 solutions where one hand is on top of the other and the direction to the 6-hour mark for both hands is the same.
EDIT: I've had another think about this, and I reckon that although the puzzle wording doesn't say so, we're probably just meant to give the exact time of the clock hands shown in the image on the puzzle page (and reproduced below)...in which case there's only one solution. It doesn't really make sense otherwise, there being so many solutions.
My Excel T&E only took a few seconds longer than a few seconds, which I was quite pleased about.
Even at my age I don't have centuries to wait for your 100-page proof to appear - and besides, I have to go to bed soon - but I'll hang around here for a bit longer in case you can get your idea to work.
All the best with it!
That works perfectly...thanks! I've never used Reduce before...hope I can remember to use it if the opportunity arises again.
bobbym's code is Mathematica, which we both have. He knows it very well, and I know some.
I don't know though how to express all these in a mathematical way.
Same here. I started on this puzzle in much the same way as what you've shown, but couldn't progress from there to a mathematical solution.
That's when I turned to T&E in Excel for the solution, and for confirmation that it was unique.
I found an answer, which seems to be the only one for whole cents.
Did it by trial and error in Excel after setting up the relationships.
Is this just any old puzzle (in which case I can post the answer), or homework (for which you'd need a solution method and workings)?
Sorry, but I don't know how you'd go about it 'properly'. Someone else might, though.