But two factors ensure that whatever imaginative formulas to extend the ceasefire are offered, it will certainly end at some point - possibly very soon.

Firstly, Hamas and its military associates in Gaza will run out of hostages to release. Secondly, the Israeli prime minister Benjamin Netanyahu is determined to wipe out Hamas.

Follow the Israel-Hamas conflict live as the latest ceasefire extension draws into the evening

And, as it stands, war in Gaza in the only way in which he and his military can imagine how it can be done.

There are likely enough civilian women and children still being held in Gaza to allow another two or three extensions to the ceasefire.

After that, Hamas - if they want to continue with it - would have to consider men, including those of a fighting age, plus soldiers for release.

The current three to one ratio of Palestinian prisoners being released for Israeli hostages has seemingly been a workable number for both sides. But releasing soldiers at that ratio would be a number unlikely to pass muster with the Hamas leadership.

In the past, 1,027 Palestinian prisoners were released in exchange for just one Israeli soldier, Gilad Shalit, for example.

If one sets aside all the many logistical and even emotional issues that colour the negotiations between these sworn enemies, the numbers issue alone means that negotiators spend hours every day thinking up solutions acceptable to both sides - albeit two protagonists who fully expect to start fighting again anyway.

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The reason for all this negotiating? Well, obviously the international community, the world generally, and certainly everyone in Israel, wants the hostages to be allowed to go home.

But the overwhelming issue is the safety and security of two million people crammed into southern Gaza with little aid, deteriorating conditions, and a looming resumption of fighting that would, in the words of the United Nations chief, continue this "epic humanitarian catastrophe".

The Israel Defence Forces have said up to two million people should move to al Mawasi as the restarting of the Gaza war seems inevitable.

Al Mawasi is a Bedouin settlement in the bottom southern corner of the Gaza Strip. It is a barren wilderness 1km wide and 14km long.

Some Gazans have been making their way there, through sand dunes, in the direction of the Mediterranean Sea.

They're looking for safety, and they hope they will find it there.

A Sky News team visited as people set up makeshift shelters, building their homes on sand - there are no floors.

The World Health Organisation says al Mawasi is a recipe for disaster, as there is no infrastructure.

The pictures our team filmed showed rubbish-strewn sand dunes, broken tarpaulin tents, and little sign of infrastructure that could support huge numbers of people.

In this small space, it already seems overcrowded. One of the new arrivals told Sky News it is already disastrous.

"Not everyone is here yet and the situation is already catastrophic, let alone if they bring everybody here - then there will be a huge catastrophe," she said.

"I swear to God already so many old people have died of diseases they couldn't survive.

"If they forcefully displace us and tell us to come here, they must at least make the place safe and, look, we are now entering winter, winter is coming into our tents. When a child is sleeping in their tent and winter comes in, what should they do?" she added, sitting on the windswept coastline.

The United States acknowledges the war will resume, but from the president and his secretary of state, what started as guidance has slowly shifted into a virtual instruction for Israel to come up with a battle plan that is different to the initial invasion in the north of the Strip. Much of the north is now a wasteland of rubble.

In contrast, the south - while damaged - is in reasonable shape, if overwhelmed with people.

Benjamin Netanyahu acknowledges the American president's concern, but he is head of a coalition that includes ultra-right-wing politicians, some of whom would happily destroy Gaza and its population, while also annexing all of the West Bank.

Destroying Hamas is the very least Netanyahu would have to achieve to keep those elements onboard.

The conundrum for him and indeed the world watching on is how he can destroy Hamas and not kill thousands more innocent civilians in the process.

In a place the size of Gaza, one must wonder if it is actually possible at all.