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The king's mages have made a discovery: they can create perfectly frictionless surfaces using a new spell. The king immediately suggests a use for this spell: Use it on areas of floor, to keep prisoners on. He hopes he'll be able to make completely inescapable prisons, without any walls or roof.

The first tests don't work very well, since the area without friction can be escaped by just blowing or throwing things until the normal floor is close enough to reach. The mages find a brilliant solution: apply the friction spell to bowl-shaped depressions in the floor. Gravity prevents normal methods from making any progress. Unfortunately, anyone who walks by can release the prisoners with nothing but a rope or stick- and the mages don't know how big the bowl should be to make escape impossible for an average person.

So, the question is: how should these bowls be designed? What should their diameter and depth be to keep any normal person in indefinitely without outside help, and what other characteristics could they ideally have to maximize their usefulness in a prison? Answers will be judged based on how impressive they would appear to citizens, and how easy they would be to upkeep.

Each bowl would hold one person, and should be of minimal size that still keeps a person in. The friction spell is accomplished through the magical process of Handwavification, and is not majorly important to the question.

The depth isn't the problem, it's the shape that matters.

A perfectly frictionless curved surface can be treated like a swing. Increasing the slide distance up to the point of exceeding the top edge just by control of weight and position. It'll take a bit of time to get used to the movement but an agile person should be able to escape a bowl of any size.

What you need to build is something more like a vase, there's a pinch before the rim such that anyone approaching it at speed is merely flung back over the bowl rather than exceeding the rim height.

Whoever wants to pull a rope to help some prisoner to escape has to rely on friction. Without friction they cannot pull.

However they could still use reaction to exert a force on the prisoners.

Therefore I would say that the most effective, practical and cost effective design is simply a well with frictionless vertical sides and bottom, and the well top covered by a grid large enough to slide down a bowl of soup and nothing more.

The king of our country is a modern monarch in outlook and has devised a very similar mode of imprisonment! Deep pits and torture tables and ordinary prisons are much too practical and pedestrian. They also fail to serve their function. The modern despot subscribes to this penal code: It is demonstrated that no criminal punishment may truly serve as neither deterrent nor punishment; for the convict never truly feared our justice nor his punishment, neither the honest man ever needed to be deterred. Therefore, let all punishment of crime be for the instruction and entertainment of the People.

Therefore, the king's mages, taking their cue from the Royal Gardners devise the following means of imprisonment: the Great Globe of Wesparion. Its particulars:

• For the perpetual imprisonment of one to four convicts let there be made a great globe of one palm thick thaumic glass;


• let the globe be made with an equatorial diameter of fifteen feet;


• let there be a neck at the upper pole four hands in diameter at the upper lip, reducing to three hands at the conjunction;


• let there be a broadening at the Great Globe's equator such that it may rest suspended upon a great ring of bronze etched with many powerful runes of doom and woe and which itself shall be suspended from the city's mighty Gibbet of Gilbras the Wise, and which has long served as the last dancing partner of many a justly punished convict;


• let there be a neck at the nether pole two palms in diameter;


• let the royal Guild of Glassblowers make forthwith the Globe and let the College of Wizards inchant the said Globe with their spells and runes of baleful purport and let the said Globe be suspended before our dread Hall of Justice.

The Globe is essentially an overlarge wasp trap, but with the nether chimney facing away from the globe rather than up into it:

Pros:

• Thick thaumic glass is unbreakable through normal means; the frictionless coating prevents the inmates from escaping


• sufficiently wide upper chimney allows (generally naked) prisoners to be slipped inside the Globe; the tapered design prevents them from slipping out again, should anyone try the old Fakir's Rope incantation


• chimney at the top allows small crusts of bread to be dropped in to the inmates, and also allows for occasional showers of fresh water for bathing & drinking


• small chimney at the bottom prevents escape of the inmates, whilst allowing for the escape of noxious fluids & solids


• clear glass, suspended in one of the great squares of the capital city provides hours of slapstick entertainment for young and old alike as the writhing mass of inmates slips, slides, sloshes and slithers about within their inescapable prison!

Cons:

• none.

Note: While in our country, we allow for several inmates to be so housed, I understand your kingdom will allow for only one. I would therefore submit that a sphere of seven or eight foot diameter will be quite sufficient. Once enhoused, none may escape, either by climbing or by jumping.

Kind of like this, only fully spherical, and also unbreakable:

You don't need to use a bowl. If anything a bowl would let the prisoner escape without any external help. A flat circular disk which is taller than the persons with their arms raised would be enough to trap them as long as you dropped them into the center.

The issue with a bowl is you as a person can change your pose, but not your center of gravity (horizontally). Since there is a slight elevation due to the curve of the bowl, a person can stick there arms out and this would cause their legs do slid up the edge of the bowl slightly. Now gravity does its magic. Since the force is no longer directly down, some of it is applied horizontally causing the prisoner to enter an eternal swinging motion. Repeat this enough and they can swing themselves out.

With a Flat disk, the person has no way to create an extra horizontal force. If they stick their arms out, their body will move slightly so that their center of gravity remains in the same place. Once they put their arms down, they will slide back into their original position. If they lie down, their center of gravity will still be in the middle of the disc, so as long as they can't reach the edge of the disc they can't escape.

There are only two issues. Dropping them onto the disk with no horizontal momentum and air resistance..

**A better version of the bowl.

Rather than have the bowl be entirely frictionless, make the base of it have friction. About 1 or 2 feet in diameter so that the prisoner can't jump out of the bowl, and they can't build up enough running speed. This way, if they try to swing out of the bowl, they hit the base and get slowed down. Even better, make it out of sand paper so they really don't want to slid into it.