The Duke of Cambridge has spoken of his "immense pride" at being associated with Cambridge as he and the Duchess toured the city.

The royal couple received a rapturous welcome from hundreds of well-wishers who lined the streets of Cambridge to greet them on their first official joint visit to the city since their marriage.

Speaking at a reception in the university's Senate House, William said he and Kate had looked forward to visiting Cambridge ever since they adopted their titles on their wedding day in April last year.

"We both feel immense pride at being associated with Cambridge, a place renowned the world over for its dynamism, beauty and learning, and it is lovely for us to be here together today," he said.

William paid tribute to the work of Cambridge University, saying its academic record down the centuries left them both feeling "very humble".

"Within a mile of us, gravity and DNA were discovered," he said.

"Many of the brilliant minds who, through their later work at Bletchley Park, did so much to save our country and the free world, were given first flowering to their genius here at Cambridge.

"This university has more Nobel prize-winners to its name than all but a couple of countries."

On a more light-hearted note, William joked at his brother's expense about their visit to Trinity College, Cambridge, five years ago.

"My brother Harry and I were fortunate enough to come to Cambridge five years ago, when we spent a couple of days at Trinity," he said.

"I have to say, it's the closest Harry's ever got to university."

Kate and William later met students and academics from Cambridge University at a marquee reception inside Senate House.

Chris Humpleby, 21, a third year undergraduate studying education at Emmanuel College, met Kate.

He said: "I think they are lovely, they don't have easy lives, to be constantly watched and judged wherever you go is difficult. I think they are amazing."

Kate also met Moos Peeters, 26, a postgraduate from the Netherlands who is studying neuroscience, who said: "All my friends were very jealous when they heard I was going to meet them."

William drew laughter too when he referred to the traditional rivalry between Oxford and Cambridge, in reference to Cambridge's record on Nobel prizes.

"That fact alone must shake even that other place along the M40 - it that must not be named - to its very foundations," he said.

Fergus Todd, 21, an undergraduate studying economics at Clare College, from Edinburgh, also met Kate at the reception. He said: "She was lovely - she was extremely good at asking questions."

During the Senate reception, Kate revealed she is a fan of the BBC quiz show University Challenge as she chatted with two Clare College students.

"I love watching University Challenge," she told economics undergraduate Fergus Todd, 20, and neurosciences postgraduate Moos Peeters, 26.

The 30-year-old Duchess asked: "Are the colleges competitive? Do you take part in University Challenge?"

Todd, who is president of his college's student union, said afterwards: "We told her absolutely not. That is for the absolute elite."

William also proved to be a fan of the quiz presented by Jeremy Paxman, telling one guest: "I watched Trinity annihilate York. I could manage one question. The brain power in here is palpable. I'm finding it quite intimidating."

Kate met a relative during the reception - Dr Penny Barton, a graduate tutor at Homerton College, who is her father Michael Middleton's first cousin and attended the royal wedding.

They greeted each other warmly and Dr Barton said after the meeting: "She did look a bit surprised, although I think she knew I would be here.

"I only saw her in the distance at the royal wedding, to be honest, but we've had another family get-together since, so we've seen her in the last year or so.

"The family is terribly thrilled and very, very proud because we think she does a good job and it's not easy walking about talking to lots of people and being genuinely interested in who she meets."

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  • Royal visit to Cambridgeshire

    The Duchess of Cambridge meets Emma Henson, 7, during a visit to Peterborough City Hospital in Cambridgeshire, as part of an official visit to Cambridge.

  • Royal visit to Cambridgeshire

    A gust of wind catches the hair of The Duchess of Cambridge as she arrives at Peterborough City Hospital in Cambridgeshire, during an official visit to Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge meets well wishers during a visit to Peterborough City Hospital in Cambridgeshire, as part of an official visit to Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge meets Dorothy West, 96, during a visit to Peterborough City Hospital in Cambridgeshire, as part of an official visit to Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge meets Sumi Willett during a visit to Peterborough City Hospital in Cambridgeshire, as part of an official visit to Cambridge.

  • Royal visit to Cambridgeshire

    The Duke and Duchess of Cambridge pose for a picture taken by patient Linda Smith, during a visit to Peterborough City Hospital in Cambridgeshire, as part of an official visit to Cambridge.

  • Royal visit to Cambridgeshire

    The Duke and Duchess of Cambridge pose for a picture taken by patient Linda Smith, during a visit to Peterborough City Hospital in Cambridgeshire, as part of an official visit to Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge meets well wishers during a visit to Peterborough City Hospital in Cambridgeshire, as part of an official visit to Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge meets Sumi Willett during a visit to Peterborough City Hospital in Cambridgeshire, as part of an official visit to Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge meets Emma Henson, 7, during a visit to Peterborough City Hospital in Cambridgeshire, as part of an official visit to Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge meets Sumi Willett during a visit to Peterborough City Hospital in Cambridgeshire, as part of an official visit to Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge during a visit to Peterborough City Hospital in Cambridgeshire, as part of an official visit to Cambridge.

  • Royal visit to Cambridgeshire

    Sumi Willett who met with the Duchess of Cambridge, during a visit to Peterborough City Hospital in Cambridgeshire, as part of an official visit to Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge meets Emma Henson, 7, during a visit to Peterborough City Hospital in Cambridgeshire, as part of an official visit to Cambridge.

  • The Duke And Duchess Of Cambridge Make An Official Visit To Cambridge

    CAMBRIDGE, CAMBRIDGESHIRE - NOVEMBER 28: Catherine, Duchess of Cambridge meets children working on projects as she visits Manor School as she pays an official visit to Cambridge with Prince William, Duke of Cambridge on November 28, 2012 in Cambridge, Cambridgeshire. (Photo by Chris Jackson - WPA Pool/Getty Images)

  • The Duke And Duchess Of Cambridge Make An Official Visit To Cambridge

    CAMBRIDGE, CAMBRIDGESHIRE - NOVEMBER 28: Prince William, Duke of Cambridge meets pupils as he visits Manor School as she pays an official visit to Cambridge with Prince William, Duke of Cambridge on November 28, 2012 in Cambridge, Cambridgeshire. (Photo by Chris Jackson - WPA Pool/Getty Images)

  • The Duke And Duchess Of Cambridge Make An Official Visit To Cambridge

    CAMBRIDGE, CAMBRIDGESHIRE - NOVEMBER 28: Prince William, Duke of Cambridge meets pupils as he visits Manor School as she pays an official visit to Cambridge with Prince William, Duke of Cambridge on November 28, 2012 in Cambridge, Cambridgeshire. (Photo by Chris Jackson - WPA Pool/Getty Images)

  • The Duke And Duchess Of Cambridge Make An Official Visit To Cambridge

    CAMBRIDGE, CAMBRIDGESHIRE - NOVEMBER 28: Catherine, Duchess of Cambridge and Prince William, Dukem of Cambridge watch a performace as they visit Manor School as she pays an official visit to Cambridge with Prince William, Duke of Cambridge on November 28, 2012 in Cambridge, Cambridgeshire. (Photo by Chris Jackson - WPA Pool/Getty Images)

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge arrives at the Guildhall in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge arrives at the Guildhall in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge on a tour of Jimmy's resettlement centre in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge on a tour of Jimmy's resettlement centre in Cambridge.

  • Royal visit to Cambridgeshire

    The Duke and Duchess of Cambridge on a tour of Jimmy's resettlement centre in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge on a tour of Jimmy's resettlement centre in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge on the balcony of the Guildhall in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge arrives at the Guildhall in Cambridge.

  • Royal visit to Cambridgeshire

    The Duke of Cambridge meets Oliver Duell, 7, at the Guildhall in Cambridge.

  • Royal visit to Cambridgeshire

    The Duke of Cambridge greets well wishers during a walkabout in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge meets Clive Marshall, 51, at the Guildhall in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge arrives at the Guildhall in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge arrives at the Guildhall in Cambridge.

  • Royal visit to Cambridgeshire

    The Duke and Duchess of Cambridge arrive at the Guildhall in Cambridge.

  • Royal visit to Cambridgeshire

    The Duke of Cambridge greets well wishers during a walkabout in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge meets James William Davies, 5 months, who was named after Prince William, with mother Tessa Davies during a walkabout in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge meets James William Davies, 5 months, who was named after Prince William, with mother Tessa Davies during a walkabout in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge arrives at the Guildhall in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge arrives at the Guildhall in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge arrives at the Guildhall in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge meets Oliver Duell, 7, at the Guildhall in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge speaks to University staff and students during a visit to Senate House in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge speaks to University staff and students during a visit to Senate House in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge speaks to University staff and students during a visit to Senate House in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge arrives at Senate House, University of Cambridge, as the Royal couple mark their first official joint visit to Cambridgeshire as The Duke and Duchess of Cambridge.

  • Royal visit to Cambridgeshire

    Young girls watch from a university window as they await the arrival of the Duchess of Cambridge at Senate House, University of Cambridge, as the Royal couple mark their first official joint visit to Cambridgeshire as The Duke and Duchess of Cambridge.

  • BRITAIN - ROYALS - CAMBRIDGE

    Catherine, the Duchess of Cambridge meets members of the public during a walk through the streets central Cambridge ahead of an event at the Senate House on November 28, 2012. Britain's Prince William and his wife Catherine visited the university city that is home to their dukedom for the first time since they were given their official titles. William and Catherine, who were given the titles the Duke and Duchess of Cambridge when they married last year, received an ecstatic welcome from hundreds of people who started lining the streets in the early hours of the morning. AFP PHOTO/Leon Neal (Photo credit should read LEON NEAL/AFP/Getty Images)

  • BRITAIN-ROYALS

    Catherine, The Duchess of Cambridge looks on during a visit to Senate House in Cambridge on November 28, 2012. Britain's Prince William and his wife Catherine visited the university city that is home to their dukedom for the first time since they were given their official titles.William and Catherine, who were given the titles the Duke and Duchess of Cambridge when they married last year, received an ecstatic welcome from hundreds of people who started lining the streets in the early hours of the morning. AFP PHOTO/POOL/Kirsty Wigglesworth (Photo credit should read KIRSTY WIGGLESWORTH/AFP/Getty Images)

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge speaks to University staff and students during a visit to Senate House in Cambridge.

  • Royal visit to Cambridgeshire

    The Duchess of Cambridge speaks to University staff and students during a visit to Senate House in Cambridge.

  • Royal visit to Cambridgeshire

    The Duke and Duchess of Cambridge arrive at Cambridge station.

  • The Duke And Duchess Of Cambridge Make An Official Visit To Cambridge

    CAMBRIDGE, UNITED KINGDOM - NOVEMBER 28: Catherine, Duchess of Cambridge meets dignitaries as she arrives at Cambridge Guildhall as she pays an official visit to Cambridge with Prince William, Duke of Cambridge on November 28, 2012 in Cambridge, England. (Photo by Chris Jackson/Getty Images)

  • The Duke And Duchess Of Cambridge Make An Official Visit To Cambridge

    CAMBRIDGE, UNITED KINGDOM - NOVEMBER 28: Catherine, Duchess of Cambridge and Prince William, Duke of Cambridge smile and wave to the crowds from the balcony of Cambridge Guildhall as they pay an official visit to Cambridge on November 28, 2012 in Cambridge, England. (Photo by Chris Jackson/Getty Images)