The Dutch state examination of mathematics for high school students includes a section with math examples on the first cryptocurrency. The text explains the principles of bitcoin mining, and students need to answer a number of questions requiring mathematical calculations.

The VWO is a six-year education stream with a focus on theoretical knowledge, that prepares students to follow a bachelor's degree (WO) at a research university. Students study the VWO at schools known as atheneum and gymnasium and complete the stream around the age of 18. In 2018, a section on bitcoins appeared in the state examination of mathematics. This was discovered by one of the Reddit users.

"The bitcoin is a digital currency that only exists online. He exists since January 1, 2009 and can be used to pay in online stores or for other online services. Bitcoins are not, as normal money, by a central bank circulation. Instead, all bitcoins that are in circulation are created by letting computers work on solutions from selected mathematical problems. That works like this: Anyone can run special software on his or her computer contributes to solving such a mathematical problem. The owner of the computer that finds the solution to a problem 25 (newly created) bitcoins as a reward. Because in 2014 every 10 minutes such a problem was solved, were there in this way every 25 minutes 25 bitcoins are put into circulation. On 1 January 2014 there were (approximately) 12.2 million bitcoins in circulation."

Here is the translations of the questions that Dutch high school students (17-18 years old, pre-university) had to make during their national mathematics (with a focus on statistics) finals.

  • Calculate, in which year the volume of bitcoins in circulation will reach 18 million, given that the speed with which they appear does not change.
  • In fact, the speed at which bitcoins fall into circulation is not 25 bitcoins in 10 minutes. This speed is reducing. During the first four years, from January 1, 2009 to January 1, 2013, the reward for solving one problem was 50 bitcoins. The award for finding a solution every four years is halved: from January 1, 2013 to January 1, 2017, the reward for one solution was 25 bitcoins, during the next four years it reduced to 12.5 bitcoins for one solution and so on. From which year will the reward for each solution be less than one bitcoin?
  • The total number of bitcoins that can be put into circulation is limited. This is a consequence (among other things) of the fact that the reward for a decision is always cut by half. The total number of bitcoins in circulation can be described by the formula: C = 21-21 * 0.5 ^ (0.25 * t), where C is the total number of bitcoins in millions, and t is the number of years since January 2009. Use the formula to determine the maximum number of bitcoins in circulation.
  • To regulate the total number of bitcoins in circulation, not only does the reward for solving one problem decrease, but the complexity of mathematical problems also increases. There are more and more people who connect their computers and start to solve these problems. The difficulty of the problems increases exponentially with the formula D = 3.65 * e ^ (0.533 * t), where D is the complexity of the problem, and t is the time in months, starting from January 1, 2013. The larger the D, the more difficult it is to solve the problem. Compose the formula of the derivative of D and explain how to handle this formula can see that the graph of D is increasing. The formula can be rewritten in such a way that you can use a difficulty level fill in and calculate the time in months needed to do so level of difficulty.