For Brian McDermott's side to reach the semi-finals of the Rugby League World Cup, a specific series of events needs to happen next weekend.
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series → reach → events
On the backfoot since being humbled 32-10 by Tonga in their opening game, England responded with a crushing 82-0 victory over France to keep their dreams alive.
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England → humble → dreams
It means England need to beat co-hosts Papua New Guinea in their final group match in Wollongong next Friday – then hope Tonga beat Samoa, two days later in Sydney.
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Tonga → mean → Sydney
If Samoa win, England will be eliminated because of their inferior head-to-head record against Tonga.
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England → win → Tonga
They will also be knocked out if Tonga and Samoa draw.
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Tonga → knock → ?
But if Tonga win, it comes down to points difference between England and Samoa.
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it → win → England
Samoa, following hefty victories over the French and PNG, is +132 – which is 68 better than England.
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which → follow → England
So, 68 is the number to remember.
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68 → remember → ?
If England beat PNG by 68 points or more, then any Tongan win is good enough for McDermott's men.
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win → beat → men
Less than 68, and they must hope Tonga are really inspired by Pacific rivalry to put one over their island neighbours.
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Tonga → hope → neighbours
England hope the numbers go in their favour to avoid an unwanted first.
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numbers → hope → first
In 16 previous Rugby League World Cups, staged in varying formats, neither England nor Great Britain have ever finished outside the top four.
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England → stag → four
And every time the format has included semi-finals, they have got there.
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they → include → finals
Group B-C: The remaining games
Fri, 30 Oct: England v Papua New Guinea: Wollongong, 09:05 GMT
Sun, 1 Nov: Lebanon v France: Parramatta, Sydney: 06:40 GMT
Sun, 1 Nov: Tonga v Samoa: Parramatta, Sydney: 09:05 GMT
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Lebanon → remain → Samoa
'I'm not sure what else we could have done'
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we → do → what
"What we have done today is enormous, given the context," McDermott told his post-match media conference in Perth.
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McDermott → do → Perth
"Knowing we had to win big - and we have had candid conversations about that this week - we have done that without getting hot.
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we → know → that
Everything was measured and planned.
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Everything → measure → ?
"Whatever the results next week, we have to finish strong - if we go home next week, we will be disappointed, but I'm not sure what else we could have done."
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we → have → what
McDermott's final comments may allude to the controversial format of this men's World Cup, which features an unbalanced group stage that has not helped England's prospects.
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that → allude → prospects
Pool A has four teams - Australia, New Zealand, Fiji and the Cook Islands - fighting for two semi-final places in a round-robin format.
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A → have → format
But Pools B and C are combined into one six-team league, from which only the top two will make the semi-finals.
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two → combine → finals
England, drawn in Pool B, play the three Pool C teams - Tonga, France and Papua New Guinea.
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England → draw → teams
It means while England are competing with Samoa for a semi-final place, they will not actually play each other.
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they → mean → other
It also means that while New Zealand lost their opening fixture against Australia, their path to the semis remains simple – win their final two group games.
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path → mean → games
England too had to win their last two pool matches but also needed snookers.
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England → have → snookers
There is some reason behind the maddening format, introduced after France – who were supposed to host a 16-team men's World Cup last summer – pulled out because of money troubles.
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who → be → troubles
Australia stepped in with New Zealand and Papua New Guinea, with the number of teams involved shrunk from 16 to 10 to cut costs.
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number → step → costs
This format also means every team plays three group games, there are no fallow weekends and the whole tournament can be done in a relatively tight five weeks.
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tournament → mean → weeks
'We have given ourselves half a chance'
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We → give → chance
But it is unquestionably harder on sides in Groups B and C. The fact Australia and New Zealand are in Group A won't help the perception of the tournament being skewed towards the southern hemisphere giants.
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tournament → help → giants
"We were the best we could be," England captain George Williams said of the France win.
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Williams → say → win
"The situation has been difficult, but we have given ourselves half a chance."
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we → give → chance
It also leaves England fans with a nagging feeling their side are only producing their best when they are already halfway home.
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they → leave → best
After a sluggish, disconnected showing against Tonga, England were slow starting against France before finding their mojo - no tries until the 23rd minute; by the final whistle they had run in 14.
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they → start → whistle
England's UK based players took nearly 48 hours to travel out to Perth.
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players → base → Perth
BBC Sport understands that the tournament organiser planned England's travel itinerary for the World Cup.
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organiser → understand → Cup
The convoluted route featured a bus journey to London, then flights via Singapore and Sydney rather than straight to Perth, where they played their first two games.
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they → feature → games
McDermott's side did not play a warm-up fixture and completed just two full training sessions before taking on Tonga.
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side → play → Tonga
"We have been together for only five field sessions; we are building something here," said McDermott.
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McDermott → build → something
…and 3 more, not listed.
The Aporia
