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The Australian Competition and Consumer Commission (ACCC) is taking Coles to the federal court testing allegations the supermarket breached the law by offering “illusory” discounts on many everyday products. Coles denies any wrongdoing. One week into the court battle, business editor Jonathan Barrett tells Reged Ahmad what we’ve learned about how discounts are set and whether the outcome could bring prices down

Every Sunday, we’ll bring you some of the Guardian’s best stories from the week. Stories we loved, that made us feel happy, sad, or just made us think, read by the people who wrote them. Writer and critic Fiona Wright has often joked with her friends that, in order for them to own homes, they’d have to wait until their parents die. But is there a truth to this dark joke?

Tony Barry and Barrie Cassidy examine new polling that shows the upcoming South Australian election could deliver a nightmare result for the Liberal party and the first test for the reported surge to One Nation. The Barries also examine Angus Taylor’s new-look shadow frontbench and the fiery political debate around returning IS families.

In his first comments after the arrest of Andrew Mountbatten-Windsor, Anthony Albanese says that the ex-prince has had an extraordinary fall from grace. And while the prime minister is a firm republican, this disgrace will not prompt another referendum. Speaking with Guardian Australia’s political editor Tom McIlroy, the PM hits back at Pauline Hanson’s comments about Muslim Australians. He also discusses what would happen if the 34 Australian wives and children of Islamic State fighters stuck in Syria made their back to Australia

Andrew Mountbatten-Windsor has been arrested on suspicion of misconduct in public office by police investigating his dealings with Jeffrey Epstein. Six unmarked police cars carrying plainclothes officers arrived at the Sandringham estate while the former prince was celebrating his 66th birthday on Thursday. Officers searched the Norfolk property as well as Mountbatten-Windsor’s former home at the Royal Lodge in Great Windsor Park. Lucy Hough speaks to the Guardian journalist David Pegg

For many Australians, the only chance they will have at owning a home will come in the form of tragedy. House prices have become so expensive that Australians are increasingly relying not just on the bank of mum and dad, but on the inheritance that comes with their death to get a foot on the housing ladder. Over the next 20 years, it’s expected $5.4tn will be passed down from baby boomers to their beneficiaries. But experts warn that this great intergenerational wealth transfer presents one of the biggest challenges the country has faced in decades. Reged Ahmad speaks with deputy features editor Celina Ribeiro about how the age of inheritance is threatening economic equality, faith in the ‘fair go’, and even in democracy itself

A group of 34 Australian women and children held by Islamic State for years without charge have been forced to return to a detention camp after attempting to flee Syria for their homeland. Reged Ahmad speaks to senior reporter and former foreign correspondent Ben Doherty on the fierce debate over their repatriation and what it means to be an Australian citizen

Extreme heat is already the most common cause of weather-related hospitalisations in Australia and with heatwaves intensifying, our climate and environment correspondent Graham Readfearn put his body to the test in an experiment. In a climate chamber at the University of Sydney, he walked on a treadmill while temperature conditions were constantly adjusted, adding direct sunlight and higher humidity. Graham joins Nour Haydar to talk about how extreme heat affects us, our cognitive functions and our chances of survival

Barack Obama has caused a frenzy after saying he thinks aliens are real during a podcast interview. The former US president was forced to release a statement clarifying he had not seen any evidence of extraterrestrials. There is a long-running conspiracy theory claiming the US government is hiding extraterrestrials at Area 51, a highly classified air force site in Nevada. Lucy Hough speaks to the host of the Guardian’s Science Weekly podcast, Madeleine Finlay

As Australians watch Donald Trump continue to crack down on immigrants, a private prison company used by ICE in the US is now running detention centres in Australia. In the US, the company faces allegations of ‘gross negligence’, and in Australia, staff inside the detention centres have highlighted safety concerns, including a rise in sexual assaults. Reged Ahmad talks to chief investigations correspondent Christopher Knaus and investigations reporter Ariel Bogle about the growing scrutiny over the Albanese government’s decision to put the company in charge of Australia’s detention regime

A recent survey has painted a damning picture of the bullying and abuse some of Australia’s coaches, referees and club officials face each week on the field – and parents are responsible for almost half of it. Sports reporter Jack Snape tells Reged Ahmad about the impact of poor parental behaviour on grassroots sport

Every Sunday, we’ll bring you some of the Guardian’s best stories from the week. Stories we loved, that made us feel happy, sad, or just made us think, read out by the people who wrote them. This weekend, unsettled by how angry our world has become, journalist and author Brigid Delaney explores what we can do to break the contagion of rage we’re seeing in our everyday lives

The Barries are back, and Angus Taylor has won the Liberal leadership battle against Sussan Ley. Speaking on Friday afternoon, the new leader said he did not seek to be ‘One Nation lite’ but he would ‘shut the door’ on people who don’t share ‘Australian values’. But the spill wasn’t the only story in Australian politics this week. Barrie Cassidy and Tony Barry unpack the challenge ahead for Taylor, the rise of One Nation and the visit of Israeli president Isaac Herzog

Angus Taylor has been elected the Liberal party’s new leader, ousting Sussan Ley in a party room ballot 34 votes to 17. Speaking shortly after the vote, Ley said she would quit parliament within weeks in a bid to provide clear air for Taylor’s leadership. In his first speech as opposition leader Taylor pointed to a greater focus on immigration policy, saying: “If someone doesn’t subscribe to our core beliefs, the door must be shut.” Political editor Tom McIlroy speaks to Nour Haydar about how it all went down and Taylor’s striking shift in tone on immigration

Protesters around Australia, including Nick McKim and other Greens MPs, gathered to express opposition to the visit of the Israeli president, Isaac Herzog, this week. The Greens senator tells political editor, Tom McIlroy, that the confronting scenes of police aggression towards protesters in Sydney was a “massive overreach”. McKim is the Greens spokesperson for economic justice and treasury, and is now leading a parliamentary inquiry into the 50% capital gains tax discount. Labor has not ruled out possible changes to the generous tax breaks for investors ahead of the May budget. The Tasmanian senator argues that, with Greens’ support, the government can “marry up the politics and the policy” to meaningfully addressing the housing crisis

After weeks of speculation, a Liberal leadership spill is set for 9am on Friday when Angus Taylor will challenge the opposition leader, Sussan Ley, for control of the party. Political editor Tom McIllroy speaks to Reged Ahmad about why Taylor is making his move now, whether he has the numbers to win, and what it all means for the future direction of the Coalition

Keir Starmer has seen off a challenge to his leadership after facing calls for his resignation over the appointment of Labour powerbroker Peter Mandelson as ambassador to the US. A man who enjoyed a close relationship to Jeffrey Epstein. Monday’s win could prove to provide only a temporary respite for the unpopular UK prime minister, as his critics continue to question his judgement and authority. Guardian Australia’s UK/US site editor Jonathan Yerushalmy speaks to Reged Ahmad about how the events of the week unfolded, whether Starmer can hold on to power and how the Epstein files have rocked British politics.

Hundreds of jobs have gone at the newspaper that broke the Watergate scandal. Was profit or politics behind the decision? Jeremy Barr reports

In Lake Cargelligo, central west New South Wales, police are hunting for an alleged triple murderer. Julian Ingram, also known as Julian Pierpoint, is suspected of shooting dead his former partner Sophie Quinn, who was seven months pregnant, her new partner John Harris, and her aunt, Nerida Quinn. He also shot and injured Kaleb Macqueen.Reged Ahmad speaks with Nino Bucci about the alleged murderer’s past domestic violence offences, and the questions that linger while the gunman is still at large.

Last night tens of thousands of people gathered in cities across the country to protest against a visit by Israel’s president, Isaac Herzog. Outside the Sydney Town Hall it wasn’t long before the protest turned violent, with video footage showing police pepper-spraying, charging and dragging protesters – including Muslim worshippers who were kneeling in prayer. Nine people have been charged after the clashes with police, with police saying more charges are expected to be laid. Guardian reporter Jordyn Beazley was there, and tells Nour Haydar when the protest turned violent and whether it all could have been avoided.