German tank problem

Imagine you are playing a game in which you have to guess the number of toy tanks a factory produces each day. As the game progresses, you start keeping track of the number of tanks produced each day.

Now, a big boss comes and tells you that he will not tell you the exact number of tanks but you can figure it out based on some clues. The first clue is that the tanks produced are numbered sequentially (like 1, 2, 3, 4…). The second clue is that you know the highest number of the tanks that were produced in a day.

So, let’s say the highest number of tanks made in a day was 29. You start tracking the number of tanks produced each day, and you find out the numbers on the tanks produced on 6 days - 3, 7, 12, 16, 22, and 28.

So, you may think that the total number of tanks produced by the factory must be somewhere around 29*(days) = 174 (29 multiplied by the total number of days).

However, this is where the German Tank Problem comes in. Based on this limited information, you can make a more accurate estimate of the actual number of tanks produced.

You see, the numbers on the tanks are sequential, so you can assume that the factory is producing all the numbers of the tanks. From the numbers you have recorded, you know that the factory has produced tank 3, tank 7, tank 12, tank 16, tank 22, and tank 28.

Now, let’s say tank number 22 is the highest number you recorded. This tells you that the factory must have produced at least 22 tanks. Furthermore, since you know that the numbers on the tanks are sequential, you can assume that there were no gaps in the sequence. Based on this, you can also assume that the factory has produced all the tanks between 1 and 22.

So, using this logic, you can estimate that the factory has produced at least 22 tanks and no more than 28 tanks because the highest number recorded is 28. If you take the average of these two values (22 and 28), you get an estimate of 25 tanks produced per day.

Thus, using the German Tank Problem, you can make a more accurate estimate of the actual number of tanks produced even if the highest number of tanks produced each day is known.