A puzzle in the Christmas card sent out by a British spy chief has successfully flummoxed around 600,000 people. The card turned out to be part of a five-stage challenge that only three people came even close to finishing.

It was the work of Robert Hannigan, the director of GCHQ. That’s the United Kingdom’s communications intelligence agency and is roughly equivalent to the NSA. The solutions have now been published.

The card, which was reproduced online, included a grid which needed to be filled in with blocks of black squares. The only information contestants had to go on was details of how long the various blocks along each line and row were.

If you’d like to give the full challenge a go, the image is shown above, so stop reading from this point! We’ll list a few example questions and put the answer at the bottom of this article.

After completing the grid, it was left to players to figure out that the result was a QR code, which led to a website revealing the next stage. This was a series of questions asking players what came next in a sequence and giving six options. One asked what came next in the sequence “GREEN, RED, BROWN, RED, BLUE, -, YELLOW, PINK?”

Selecting the correct answers to all of these brought up a series of word puzzles, with the four correct answers creating a URL to advance. One example here was a question explaining that if “agony” is the opposite of “denial”, “witty” the opposite of “tepid” then what is the opposite of “smart”?

Follow the URL and you got a series of missing number sequences, one of which was “2, 4, 8, 1, 3, 6, 18, 26, ?, 12, 24, 49, 89, 134, 378, 656, 117, 224, 548, 1456, 2912, 4934, 8868, 1771, 3543”

Solve those and figure out that the list of answers created an IP address and you got to the final round, which involved 11 diverse puzzles. They’re too detailed to explain here, but suffice to say that to complete them you’d have to figure out (among many other points) that:

• auto, prim and son are all the start of the names of Doctor Who creatures (Autons, Primord and Sontarons);

• x can be an algebraic letter, a multiplication symbol and a Roman numeral;

• a series of nine clues produced answers which were the names of Lord of the Rings fellowship members plus two extra letters;

• all of these extra letters spelt out Shire Dragon Tricker, which corresponds to Bilbo; and

• a wordsearch included answers such as “HRVATSKA” and “ESWATANI” which are the names of countries in that country’s main language.

While GCHQ has previously used puzzles to recruit new staff, this appears to be just a bit of evil fun. There’s no word on what would have happened if anyone solved the entire thing, but the three people who came closest will get the somewhat unspectacular prize of a paperweight and a biography of Alan Turing.

And the answers to the questions we’ve listed?

• With the color sequence, it turned out the answer was blue because the colors reflect the digits in pie and the corresponding color ball that carries that score in snooker. (The dash represents nine, which doesn’t have a corresponding ball.)

• With the words, the opposite of “smart” was “often”. That’s because when written in Morse code, each dot in one word is a dash in the same position in the other word, and vice versa.

• With the numbers, the missing answer was 52. That’s because the list showed alternate digits from each entry in the list of powers of two, hence: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384 and so on.