We know that the Triwizard cup itself was Summonable. After all, Harry did Summon it in the graveyard.
So why didn't any of the contestants Summon it while in the maze?
Canonical answers, please.
Science Fiction & Fantasy Stack Exchange is a question and answer site for science fiction and fantasy enthusiasts. It only takes a minute to sign up.Sign up to join this community
This answer probably won't be the conclusive canonical answer that Mithrandir is looking for. The issue isn't clearly addressed in the books, however, so it's difficult to be definitive. There are two options.
This is probably the most likely option. Similar charms were placed by Voldemort on the cave in which he hid the locket in order to protect the Horcrux.
Harry had not expected this, but cleared his throat and said loudly, wand aloft, “Accio Horcrux!”
With a noise like an explosion, something very large and pale erupted out of the dark water some twenty feet away; before Harry could see what it was, it had vanished again with a crashing splash that made great, deep ripples on the mirrored surface. Harry leapt backward in shock and hit the wall; his heart was still thundering as he turned to Dumbledore.
“What was that?”
“Something, I think, that is ready to respond should we attempt to seize the Horcrux.”
(Half-Blood Prince, Chapter 26, The Cave).
Putting anti-Summoning Charms on the Cup would simply be a prudent preventative measure to ensure fair competition on the part of the Ministry. Considering that Barty Crouch, Ludo Bagman and others had spent many months (if not years) preparing for the Tournament I'm sure that they would've thought of such a simple defensive precaution.
It's true to say that the Cup was Summonable in Little Hangleton. Any protective charms may well have applied to the geographical area (i.e. the maze) rather than to the object itself, as tobiasvl says. Since nobody apart from Crouch Junior ever expected the Cup to leave the maze it's reasonable to suppose that any anti-Summoning charms would just apply to the maze and not to other locations.
If it was possible to summon the Cup then the fact that no-one took advantage of the loophole can be put down to nobody attempting to use a Summoning Charm in the maze. It's possible that the contestants simply assumed that anti-summoning protections applied to the Cup and so didn't bother to waste time with a spell they thought would be ineffective.
Remember too that two of the contestants, Fleur Delacour and Victor Krum, were out of action for part of the Third Task. With Crouch Junior cursing contestants from outside the maze they were not able to perform at their peak.
“You had an easier time of it than you should have in that maze tonight, of course,” said Moody. “I was patrolling around it, able to see through the outer hedges, able to curse many obstacles out of your way. I Stunned Fleur Delacour as she passed. I put the Imperius Curse on Krum, so that he would finish Diggory and leave your path to the cup clear.”
(Half-Blood Prince, Chapter 35, Veritaserum).
Most likely explanation: The Cup was Summonable in Little Hangleton but not in Hogwarts because of protective charms placed on it by the Ministry.
There is no mention in the book that anyone tries "Accio" and therefore it is unknown if the cup is in fact summonable even during the Triwizard game (after Barty Crouch manipulated it and noone tries the easy way because everyone is absolutely convinced that summoning is no option) or if the plinth on which it stands would prevent summoning.
We don't know.
We don't know if it could be Summoned; as pointed out in the comments to the question, nobody tried to Summon it, and so we don't know why nobody tried it either, if that's your actual question. Perhaps the contestants were informed (off-camera) that the objects to retrieve in the tasks could not be Summoned, explaining why nobody tried it (but not explaining why Harry then thought to try it in the graveyard, apart from a desperate attempt in the spur of the moment).
So let's assume the Cup couldn't be Summoned in the maze. It seems the most likely scenario, and here are some guesses on how that could be possible.
The most likely possibility, in my opinion, is that the Triwizard Cup was behind a Shield Charm. This class of charms, Protego, creates an invisible barrier that deflects spells. In the books and especially the movies, Shield Charms are usually cast in duels and portrayed as barriers that the caster conjures up between themself and an attacker, and which they have to continually keep up with their wands and concentration. From Harry Potter and the Goblet of Fire, Chapter 31:
He was still having trouble with the Shield Charm, though. This was supposed to cast a temporary, invisible wall around himself that deflected minor curses
(Yes, Harry actually learns this spell as preparation for the third task of the Triwizard Tournament, conveniently introducing it right before the scene in question.)
However, they have also been shown to be able to protect a specific object or area (semi-)permanently. Of note, Fred and George Weasley sold protective clothing or "magical armor" that was charmed with permanent Shield Charms. From Harry Potter and the Half-Blood Prince, Chapter 6:
“We’ve just developed this more serious line,” said Fred. “Funny how it happened . . .”
“You wouldn’t believe how many people, even people who work at the Ministry, can’t do a decent Shield Charm,” said George.
“ ’Course, they didn’t have you teaching them, Harry.”
“That’s right. . . . Well, we thought Shield Hats were a bit of a laugh, you know, challenge your mate to jinx you while wearing it and watch his face when the jinx just bounces off. But the Ministry bought five hundred for all its support staff! And we’re still getting massive orders!”
“So we’ve expanded into a range of Shield Cloaks, Shield Gloves . . .”
And although they're not confirmed to be Shield Charms/Protego variants, other objects are also similarly permanently protected from using charms such as the Summoning Charm. From Harry Potter and the Deathly Hallows Chapter 10:
“There’s an easier way,” said Hermione, as Harry wiped his inky fingers on his jeans. She raised her wand and said, “Accio Locket!”
Nothing happened. Ron, who had been searching the folds of the faded curtains, looked disappointed.
“Is that it, then? It’s not here?”
“Oh, it could still be here, but under counter-enchantments,” said Hermione. “Charms to prevent it being summoned magically, you know.”
“Like Voldemort put on the stone basin in the cave,” said Harry, remembering how he had been unable to Summon the fake locket.
This, however, does not explain how the Cup could be Summoned by Harry later, in the graveyard. Luckily, a different and/or stronger version of the Shield Charm, Protego Totalum, is used to similarly protect certain areas over time. Both Harry and Hermione use this incantation to protect their camp; the place, not the physical tent, as shown in Harry Potter and the Deathly Hallows, Chapter 14:
“If we’re staying, we should put some protective enchantments around the place,” she replied, and raising her wand, she began to walk in a wide circle around Harry and Ron, murmuring incantations as she went. Harry saw little disturbances in the surrounding air: It was as if Hermione had cast a heat haze upon their clearing.
“Salvio Hexia . . . Protego Totalum . . . Repello Muggletum . . . Muffliato . . . You could get out the tent, Harry. . . .”
However, this charm seemingly also protects the area physically, which is clearly not the case with the Triwizard Cup, but it's possible this is the result of another of the many enchantments Hermione clearly cast around the place (although none of the ones quoted above have that effect). From Chapter 15:
She was impeded by her own Shield Charm; by the time she had removed it he had already stormed into the night. Harry stood quite still and silent, listening to her sobbing and calling Ron’s name amongst the trees.
There's precedence for believing that creating a permanent Shield Charm around an area also does require an additional charm, Fianto duri, which either allows the caster to keep a charm active while doing other things or makes a Shield barrier permanent; this was apparently used by Filius Flitwick in the movie Harry Potter and the Deathly Hallows: Part 2 to set up a Protegus maxima (a third type of Shield Charm) barrier around Hogwarts Castle before the Battle of Hogwarts.
The Triwizard Cup could possibly also have been enchanted with an Anti-theft Charm. This charm (or group of charms) is specifically to keep objects from being Summoned by anyone but their rightful owner. Perhaps the Triwizard Cup was enchanted to consider the first person to touch it as its owner, explaining how it could be Summoned by Harry later in the graveyard. Yes, this is speculative, and the Anti-theft Charm is also of dubious canonicity, having only been mentioned (I believe) in Wonderbook: Book of Spells, a video game/augmented reality book released for the PlayStation 3, in which JKR was credited for "Words and Creative Thought".
I'll just include this part for completion, although it's not the answer. Using the Summoning Charm is said to require the caster to concentrate on the object clearly in their mind. First I thought this might be the reason, but then I read this answer, which debunks that. Also, the Triwizard Cup has existed since 1294 for the first Triwizard Tournament, so anybody who's done some preparation could have done that (especially students at a school that recently held the Triwizard Cup).
It was against the rules of the third task.
The objective of the first task was to test champions' ingenuity and courage. It was an intent that participant's hadn't known what they would face until the very start of the competition. As Mr. Crouch said after the contestants were chosen by the Goblet of Fire:
"The first task is designed to test your daring," he told Harry, Cedric, Fleur, and Viktor, "so we are not going to be telling you what it is. Courage in the face of the unknown is an important quality in a wizard...very important....
Obviously things didn't happen as intended and all champions learned about the dragons beforehand, but that was an open secret. So, using the Summonning Spell to get a broomstick was found as a symptom of cleverness and cold blood. Moreover it was only a helper, the real work by Harry was to show his flying skills and outsmart a dragon to grab the golden egg.
However, Bagman told the participants directly about the principles of the third task a month before.
"That's right!" said Bagman. "A maze. The third task's really very straightforward. The Triwizard Cup will be placed in the center of the maze. The first champion to touch it will receive full marks."
"We seemply 'ave to get through the maze?" said Fleur.
"There will be obstacles," said Bagman happily, bouncing on the balls of his feet. "Hagrid is providing a number of creatures...then there will be spells that must be broken...all that sort of thing, you know. Now, the champions who are leading on points will get a head start into the maze." Bagman grinned at Harry and Cedric. "Then Mr. Krum will enter...then Miss Delacour. But you'll all be in with a fighting chance, depending how well you get past the obstacles. Should be fun, eh?"
The whole thing about the third task was to find a way to the center of the labyrinth and overcome the prepared obstacles. And there was a time difference between participants' start. If the first one to get into the maze just summoned the Cup it would probably be considered impermissible shortcut and the person wouldn't get the full marks for this task.
In his speech at the opening of the tournament Dumbledore makes the following statement:
“As you know, three champions compete in the tournament,” Dumbledore went on calmly, “one from each of the participating schools. They will be marked on how well they perform each of the Tournament tasks and the champion with the highest total after task three will win the Triwizard Cup. The champions will be chosen by an impartial selector: the Goblet of Fire.”
According to this, each champion receives a score for each task based on how well they have performed the task. The "task" of the Third Task is to get through the obstacles to the center of the maze. Simply summoning the cup would probably earn you a score of zero, because you haven't performed the "task".
Elsewhere I have argued that the tournament is not so straightforward, and there might be conflicting accounts of how one wins, but if we take Dumbledore at his word it would seem possible to summon the cup and still not win.
Although (as also mentioned in the linked question) Bagman seems to imply that the task actually consists of touching the cup, one could argue that he is assuming that one touches the cup by getting to the middle of the maze. In such a case, touching the cup is the evidence that you performed the task the best. But he might agree that if you somehow touched the cup without getting to the middle of the maze then it would not count as completing the "task" and you would not win.
Thus, it may be that no one summoned the cup because there was nothing to be gained by summoning the cup.