In this cache we try to dive a little bit into one of these problems. We will do this by making a virtual journey through the Netherlands. During this journey we will visit several places which have a connection with mathematics. The coordinates of these 'mathematical' places can be found by solving several puzzles. The final puzzles to be solved bring us a little bit closer to one of the famous millennium prize problems.
Let us start our journey by visting a place which played a role in mathematics for several hours a couple of years ago (at the beginning of 2008). In this place we could possibly chat and drink a little bit and it is named after an important mathematician. One of the things this mathematician discovered was the two dimensional surface.
Now let us investigate the place we are talking about a litte bit closer. Besides chatting and drinking it is also possible to listen to some music here. In order to be able to continue our journey we will have to break the following code.
(21, 15, 7, 29, 12, 3, 18, 7, 20, 23)
Use a [10,6]-code over F31 to find the solution. Keep in mind that the second 7 in this code (so the 7 between 18 and 20) really should be treated as a 7.
Now we have come to a place where we go for a walk. At some point during that walk we stop and have to solve the next three puzzles.
- Find the smallest value of n such that the following proposition is true: the number of times that M(n) equals 27 is 2150.
- Now find the X-coordinate value for the (local) maximum and round it to the nearest integer value.
- From the X-coordinate value you found, subtract the number of primes which are smaller than or equal to 652241.
Now, have you solved one of these prize problems? We 're afraid not.
If you 're not convinced then for instance have a look at the mathematical work of Odlyzko and te Riele (1985).
However, if your calculations are right you will probably find something you appreciate as well ...
Good luck.
You could check your solution for this puzzle here .