Very smart post indeed Tickle&Rose. I'm impressed.
And of course, I think you are very right in what you posted there.
But you know, there is always more than just 'one' right answer and more than just Maths to explain the universe as well.
Let's take Russia & China. How would you go about voiding them (defeating them) Politically and Militarily?
Easy. Make them War against each other.

The two 'bad guys' cancelling each other out.
With Israel and HAMAS. Israel can afford to drag it out. Hamas can't. Hamas Moslems are going against their Mohommedistic nature in attacking Israel and are in a race against time. Soon all of Islam will do to the French, what the Germans did to the Jews. They will extract their Christian Sacrificial 'Messiah' out of France to die for their Moslem sins. Hitler the Prophet offset the Messiah Jesus. So too will a Messiah for the Moslems offset their Prophet Mohommed. What goes around, comes around.
When Islam (as a Military Empire) gets its Messiah - it will fold as an Empire and lay down its 'weapons'. Moslems will thus become 'unarmed' and like the wandering Jews of old.
Hamas will cease to exist, forced to comply with all other Moslems in their new existence. While the unarmed wandering Jews of old, are now rising as a Military entity and in the future will be the New 'Empire' of the Middle-East.
In short.
What the Germans did to the Jews.
The Moslems will soon do to the French.
Then the Italians (Mafia+Vatican) will genocide the unarmed and vulnerable Moslems by the millions. Of course, the Moslems will pray to Allah for salvation and beg to the world for help (but past transgressions like Terrorism and Jihads won't be forgotten) - but the world will turn a blind eye. Only one nation will come to their aid and save them - ISRAEL. Ironic huh?

Israel, by then will be more Militarily powerful than it is currently and it will destroy Italy (Mafia/Vatican).
Thus Christianity in Germany has already been broken. Soon Christianity in France will burn like a Notre Dame cathedral and Christianity (Vatican) will be destroyed by its own deal with the Mafia devil. Thus, only Great Britain will remain of the Big 4. But by the time Great Britain's Christianity is taken to the Test. Israel and Islam will be 'United' (amazing huh?

) and Great Britain must 'carry its Union Jack cross' and make the ultimate sacrifice to make Israel and Islam into 'Istari' (I-star-I: The Star of David between the two Pillars of Heaven in accordance with the Koran).
Basically, this is how it will be. It's a future that can't be denied or escaped from. Even a Muppet (The Dark Crystal) can see it coming.

.
So, with this said. Hamas will fail and self destruct. Israel doesn't need to 'conquer', it only needs to prevail and not be defeated, etc. Terrorism in itself is nothing more than the last vapors of a once glorious Empire. When Islam soon turns to its last great Jihad against Christianity (the death of 'christian' France), Hamas won't be receiving any support from the likes of Iran or any other Moslem nation or entity. Hamas will implode. This is why you see Palestinians around the world showing they still 'exist' like how the Jews did - homeless, for Palestine as a nation will cease to exist by its own hand. The process you could say, is half-way there.
Islam falls from being an Empire but rises into the Garden of Religion. Jews fell from the Garden of Religion, but now Rise into being the premier Empire of the Middle-East.
...it's all just a process.
Why? Well that takes a lot to explain - but you I can say that the discovery/colonisations of the New Worlds are having an effect of 'change' upon the Old Worlds.
As a Jew myself, I can easily explain the cause of Nazi Germany and why it did to us Jews what it did. We are as much to blame for our 'holocaust' as anyone else. Nazism was our 'Frankenstein' Monster and as the humbling joke goes: What was Jesus's last words to his Jewish people when nailed to a cross?
"Wait till my little brother Hitler gets you - you bastards!
" What goes around, comes around. Redneck Prophets and Gay Messiahs... oh look! As I have said for years on this Forum. France's next President is 'Gay'. A fitting 'Messiah' for the Moslems don't you think Tickle&Rose?

Thus you are mathematically right with Israel. Currently it is not sustainable or even feasible to obliterate HAMAS by its own means. But by not allowing HAMAS to 'regain' what it has already lost, Hamas will eventually collapse in on itself like a star that has run out of hydrogen and then helium. It too cannot sustain much in the manner of what it first tried to achieve - which is all that Israel needs to do.
Judaism is the Middle-East's theme on Asia (the Holy City)
Mohommedism is the Middle-East's theme on Africa (the Holy Land).
Christianity is the Middle-East's theme on Europe (the Holy Ghost).
With the emergence of the New Worlds into the consciousness of the Old Worlds. Old Religions are falling back upon their pasts. In the end - Israel and Islam will cease to exist, as Istari will remain. As too will Christianity.
They will be relics upon Museum shelves and their books will be found in Libraries among many others. For the 'Empire' of the Middle-East will be ruled (wait for it

) by a Zoroastrian (Greek word).
So, I know you want to ask. How do I know or come about all this? Well, I've run out of type limit characte