GCHQ reveals answers and winners of Christmas puzzle

Three men have come close enough to solving GCHQ's taxing Christmas puzzle that they have been declared the winners.

The five-round challenge started last year, with a complex grid-shading teaser released in a Christmas card from Robert Hannigan, the director of the British intelligence and security agency, and demanded a mix of mathematical, linguistic and problem-solving skills.

The three winners have been named as David MacBryan, 41, from Edinburgh; US-born Kelley Kirklin, 54, from London; and Wim Hulpia, 40, from Lovendegem in Belgium.

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MacBryan, who is originally from Dublin, told the BBC: "The more puzzles you do, the better you get at doing puzzles – and I have done a lot of puzzles. I am a bit of an addict."

The men beat more than 600,000 other amateur cryptographers to win the final prize – a GCHQ paperweight and a copy of a biography of Bletchley Park codebreaker Alan Turing signed with a personal message from Hannigan - as well as "major bragging rights", said the agency.

"Many people worked in virtual teams over various web forums to tackle many of the questions together, with some syndicates developing small computer programmes to test possible mathematical combinations and reach a solution more quickly," said GCHQ, in the foreword to a document containing a complete set of the solutions.

One of the cryptographers who helped to design the puzzles said it was difficult to judge how hard to make it without knowing how many – or few – people would have a go. "In fact when tens of thousands, maybe hundreds of thousands of people were actually looking at it, we were really surprised," they said.

GCHQ has denied the puzzle was a recruitment tool, but said the winners were "welcome to apply for jobs".

The 23-page answer sheet can be downloaded via the GCHQ website.

Can you solve GCHQ's Christmas card puzzle?

10 December

The British intelligence and security agency GCHQ has released a Christmas card with a cryptic twist.

Alongside the traditional Christmas nativity scene, GCHQ director Robert Hannigan has placed a complex grid-shading puzzle within the card.

Those not on the agency's Christmas card list can attempt the brainteaser on the GCHQ website.

Successful codebreakers will uncover an image in the grid that leads to a series of tougher challenges. Any member of the public who completes all the stages of the puzzle is being asked to send their answer to GCHQ in January.

The winner will then be drawn from all the successful entries and notified soon after. The world has been confounded by a spate of maths questions on the internet this year, along with optical illusions such as the infamous 'Dress'.

How to play

• Each square is either black or white. Some of the black squares have already been filled in for you.
• Each row or column is labelled with a string of numbers. The numbers indicate the length of all consecutive runs of black squares and are displayed in the order that the runs appear in that line. For example, a label "2 1 6" indicates sets of two, one and six black squares, each of which will have at least one white square separating them.
• Complete the grid with a black pen.