The world's hardest games and puzzles: solutions and clues

WARNING: These are the answers to six brain-taxing puzzles, which you can find here.

1. Tricky Bongard problem

This conundrum continues to stump the wisest of puzzle buffs. However, there is some information here to help solve it.

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2. Boolos question

Puzzlers extraordinaire Brian Rabern and Landon Rabern, from the University of California, have kindly shared what they describe as the "simple solution to the hardest logic puzzle ever" in an eight-page answer here.

3. World's hardest Sudoku

After taking three months to create, here is the solution to the world's most difficult Soduku:

4. Einstein's riddle

Four internet gamers, known as the PoETheeds, claim to have cracked Einstein's riddle in this video:

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5. GCHQ

This is how the completed GCHQ puzzle should look when the correct boxes are shaded in black. However, the puzzle does not end here. The image is a QR code that, when scanned with a smartphone, will take you to the next step. There are five steps in total. However, more than a month after GCHQ set its "fiendishly difficult 'fun' Christmas quiz", not a single person has managed to get all of the answers right, says the Daily Telegraph. The newspaper offers help with the other four steps here.

6. Dot-town suicide riddle

Peter Winkler, professor of mathematics and computer science at Dartmouth College, explains the answer to the Dot-town suicide riddle, along with several other puzzles in a five-page paper here.