Question

Use the code provided in the template to download the string which contains the first one million decimals of T (thus, the string starts with 1415926535897932384). Write a function count_two which returns the list how_many_times, defined as how_many_times[j] = the number of times the string j appears in the first one million decimals of T, where j = 00, 01, 02,... 10, 11,... 99. In other words, chop up T-3 = .1415926535...1058209... into two-digit numbers with leading zeros included: 14, 41, 15, 59, 92, 26, 65, 53, 35., 10, 05, 58, 82, 20, 09, and so on, and count how many times they appear. how_many_times[45] is equal to the number of times 45 appears in this list. Identify the two-digit string (number) that appears most often within the first one million decimals of T, and the two-digit string (number) that appears least often. In each case, say how many times they appear. [Optional, not for credit: Print the list how_many_times, and look at the values in it. What does this tell you about the distribution of two-digit numbers (from 00 to 99) within the decimals of T?]

Answer 1

To count the number of times a two-digit number appears in the first one million decimals of T, extract the numbers and update a counter for each number. Identify the number that appears most often and least often. Examine the 'how_many_times' list to understand the distribution of two-digit numbers within the decimals of T.

Step-by-step explanation:

To count the number of times a two-digit number appears in the first one million decimals of T, we need to extract all the two-digit numbers from T and count how many times each number appears. The code provided in the template can be used to download the string containing the first one million decimals of T. We can then use a loop to iterate through the string, extracting two-digit numbers and updating a counter for each number. The resulting count can be stored in a list where the index represents the two-digit number.

After counting the occurrences of each two-digit number, we can identify the number that appears most often by finding the index with the highest count. Similarly, we can find the number that appears least often by finding the index with the lowest count. By accessing the corresponding values in the 'how_many_times' list, we can determine the exact count of each number.

By examining the values in the 'how_many_times' list, we can observe the distribution of two-digit numbers within the decimals of T. Some numbers may appear more frequently, indicating a higher probability of occurrence, while others may appear less frequently, indicating a lower probability.