Earn $6m solving 6 of the hardest mathematical problems of all time, or simply solve these easier ones for ‘fun’

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Hardest mathematical problems in the world

If you work in finance you probably have some aptitude for mathematics. Some of you will even have an exceptional mathematical talent. It's worth remembering, therefore, that $6m is still on the table from the Clay Mathematics Institute's Millennium Prize. Over 14 years after the prize was announced, just one of the seven problems has been solved. Each problem comes with a prize of $1m. What better way to compensate for falling compensation in finance?

The problems are listed on the Clay Institute's website, here.  Only the last one - the Poincaré Conjecture, has been solved. Grigori Perelman, the reclusive Russian mathematician who found the solution famously turned down the dollars, stating that he wasn't interested in money or fame and didn't want people staring at him, "like an animal in a zoo."

Self-evidently, solving any of the other Millennium Prize questions will take a lot longer than a few weekends between now and bonus time. The Poincaré conjecture was first postulated in 1904 and it took 98 years before Perelman solved it 2002. The Clay Institute then took another four years to validate his proof, making the payment deferral far worse than any bonus - assuming Perelman actually wanted to get paid.

If you're disinclined to spend the next 2,000 weekends tackling the 150-year old Riemann hypothesis or the Hodge Conjecture in pursuit of a million dollars, you can always spend a few moments this weekend solving the far easier problems below for the hell of it. Add your answers to the comments box at the bottom of this page for peer review. The first two are comparatively easy. The second two are comparatively harder.

1. You are making chocolate chip cookies. You add N chips randomly to the cookie dough and you randomly split the dough into 100 equal cookies. How many chips should go into the dough to give a probability of at least 90% that every cookie has at least one chip? (Source: Heard on the Street, Timothy Falcon Crack)

2. You have two string-like fuses. Each burns in exactly one minute. The fuses are inhomoegenous, and may burn slowly at first. the quickly, then slowly, and so on. You have a match and no watch. How do you measure exactly 45 seconds? (Source: Heard on the Street, Timothy Falcon Crack)

3. Isaac is planning a nine-day holiday. Every day he will go surfing, or water skiing, or he will rest. On any given day he does just one of these three things. He never does different water-sports on consecutive days. How many schedules are possible for the holiday? (Source: British Maths Olympiad 2013)

4. Every diagonal of a regular polygon with 2014 sides is coloured in one of n colours. Whenever two diagonals cross in the interior, they are of different colours. What is the minimum value of n for which this is possible? (Source: British Maths Olympiad 2014).

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