Problem 19: How many Sundays fell on the first of the month during the twentieth century?

Problem 24: The lexicographic permutations of 0, 1 and 2 are:

012 021 102 120 201 210

What is themillionthlexicographic permutation of the digits 0,1,2,3,4,5,6,7,8 and 9?

Problem 60: The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and concatenating them in any order the result will always be prime. For example, taking 7 and 109, both 7109 and 1097 are prime. The sum of these four primes, 792, represents the lowest sum for a set of four primes with this property.

Find the lowest sum for a setJust some examples of questions posed by Project Euler, a list of 373 mathematical programming exercises (and counting).offiveprimes for which any two primes concatenate to produce another prime.

Some are quite challenging, some are rather easy. But with the easier ones it's often still fun to find a solution that's nice and efficient. And a 'good' solution should give the answer in less than a minute. The number of Sundays in the 20th century, from the example above, happens to be *very* simple to approximate accurately, by just taking 1/7th of the total number of days.

I challenged myself to solve them all in one month. So far I've been working in Python, but maybe I can use this as an excuse to learn some new languages. Current status: 22 down, 314 to go!

**Update November 2011**: Well, one month was just a little overoptimistic. But I've made slow but steady progress, having currently solved nearly a hundred problems. They do get a lot more difficult than the examples I gave though.

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