In the list of issues for the final state examination in mathematics in the Netherlands in this year included tasks about bitcoin. Just the section about bitcoin consists of five assignments that are closely related either to each other or with the “Preface” to him.

Redditor under the name reginarhs made(a) translation preliminary information in the model test, as well as the texts of the problems. In the introductory part provides a brief squeeze about the nature of BTC and its use:

“Bitcoin is a digital currency that exists only online. It appeared January 1, 2009 and can be used to make purchases in online stores and other online services. Bitcoin, unlike conventional money, not issued by the Central Bank. Instead, all existing bitcoins are created during the solution computers special kind of mathematical problems. The following occurs: any one can run on your PC special program for the solution of such problems. A user whose computer will find the answer faster than the others, gets 25 newly generated BTC”.

This is followed by the questions themselves. In addition to the translation, reginahrs also published(a) their solutions.

  • In 2014 the answer to each task was 10 minutes, hence every 10 minutes the total stock of bitcoins was supplemented with 25 units. January 1, 2014 this stock was approximately 12.2 million BTC. Calculate what year it will be released 18 million BTC, provided that the rate of generation does not change.
  • In fact, the increase in BTC are not equal to 25 units over 10 minutes. Until January 2013 the reward was 50 BTC, and since then every four years it is reduced by half… Calculate the year in which the amount of compensation will be less than one bitcoin.
  • The total amount of bitcoins is finite. Partly because of this decreases the size of the awards. The number of bitcoins currently in circulation, can be calculated using the equation: C = 21 — 21 * 0.5^(0.25*t), where C is the number of bitcoins in millions and t is the number of years since January 2009. Find the maximum possible volume of bitcoins.
  • This volume is governed not only by reducing the awards, but also through the progressive complexity of mathematical problems. This is due to the fact that the number of users trying to solve them, is also growing. The complexity of the task (D) grows exponentially according to the equation: D = 3.65 * e^(0.533*t), where t is the time in months from 1 January 2013. A higher ratio of D implies a higher level of complexity of the task. Write the equation for the derivative D and prove that D — increasing function which is in direct proportion to the speed of mining.
  • The formula for the complexity given above can be rewritten to find the number of months during which D will acquire a value. Adapt the original equation to perform this task.

In the comments to this post user loobooloo noted(a) that the questions for exams are created two years in advance.

This is not the first case where bitcoin becomes part of the educational process. Earlier it became known that the chamber of Commerce of Dalit (DICCI) has launched in 30 cities of India training programme on mining BTC.