# The colonel who played chess

During my visit to St. Petersburg I met Tschigorinsky, the Russian chess expert, who told me that at the beginning of the Russian-Japanese hostilities, he was appointed commander of an army division where there were 20 regiments in continuous formation process, since he 100 men added weekly to each regiment.

On the last day of each week, the regiment that had the largest number of men was sent to the front.

It happened that at the time when the first regiment had 1000 men, the second had 950, the third 900, and so on, decreasing 50 men to the twentieth, who was only 50, General Tschigorinsky, discovered that the colonel of the fifth ( he had 800 men) was a great chess player.

Thus, in order to prevent being sent to the front, a fact that would occur in five more weeks, he added only 30 men each week instead of the 100 that were assigned to each of the other regiments.

Assuming that there are permanently twenty regiments forming, Can you tell how many weeks passed before our chess colonel was sent to the front?

#### Solution

The Fifth Regiment will be exceeded by the other 19 regiments, leaving the chess player with 1,370 men in his regiment. It will require 18 more weeks, adding 30 men per week, for this regiment to pass the 1,900 men now needed; so that 37 weeks, with 1,910 men is the correct answer.