I am not totally certain as I have not tried this before. Ice melts more easily as you put pressure on it. Hence the string can cut into the ice. Although the ambient temperature is more than zero degrees, the ice itself can still be -10 degrees. Hence, the water on top of the string will refreeze.
Just a thought. No coin fairs, no room bidding in auctions, less lots being assigned etc. Will there simply be much less new stock on the market in the next 6 months?
Yes, I too realised the angle would be an additional variable. The first idea to come to mind is to express sin (angle) in terms of length and radius. But then it will get messy and rearranging to get the ratio of length/radius might be difficult or not feasible.
I was thinking of doing it by a different way. The area of sector + the areas of the 2 segments. Rather curious if we can still remember the A level maths done decades ago. But on second thought, I would rather make some lunch instead.
I am not certain I follow you. You pick a random robot and ask "Which door would the other robot say is the safe door?" If you have picked the truth telling robot, he will point to the death door (assuming he knows the other robot always lies). If you picked the lying robot, then he would also point to the death door (because he knows that the truth telling robot would point to the safe door and so he lies and point to the death door). Either way you go through the other door.
A more tricky chess puzzle. White to move and wins material permanently by move 3. Material means the number of points. Queen = 9, Rook = 5, Bishop and Knight =3, Pawn =1.
Turn on switch one for 5 mins. Then turn off and turn on switch two. Then open door. The bulb which is hot and off is controlled by switch 1. The bulb which is on is switch 2. The bulb which is off and cold is switch 3.
Or you can just look through the gap at the bottom of the door or the key hole.
Turn both over. When the sand empties on the 7 mins hourglass, immediately turn it over again. Whe the 11 mins hour glass empties, the 7 mins hourglass now has 4 mins of sand. Turn that over to get the 4 mins needed.