You are given an integer, perhaps a very long long integer, composed of only the

Question

You are given an integer, perhaps a very long long integer, composed of only the digits 1 and/or 2. You have the ability to change a 1 digit into a 2 and a 2 digit into 1 and must determine the minimum number of changes that you can make resulting in no 2 digits remaining in the number that are in a position (in terms of powers of ten) higher than any 1 digit. Enter initial configuration: 2222212 Changes: 1 Note: When the only one digit is converted into a two digit the requirement is satisfied. Enter initial configuration: 11111211 Changes: 1 Note: When the only two digit is converted into a one digit the requirement is satisfied. You could also change the two 1 digits into 2 digits but that would require two changes. We want to determine the minimum number of changes necessary. Enter initial configuration: 2211221 Changes: 3 Converting all of the 1 digits into 2 digits requires the least amount of work. Enter initial configuration: 1122112 Changes: 2 Enter initial configuration: 21112221 Changes: 2 Note: Change the first 2 to a 1 and the last 1 to a 2. Enter initial configuration: - 123 Error! Please try again! Enter initial configuration: 123 Error! Please try again! Enter initial configuration: 2113221 Error! Please try again! Enter initial configuration: 21212 Changes: 2 Note: No negative values! No numbers that contain digits other than 1 or 2.

Explanation / Answer

The answer is 2, because it's closest to
1111111122222222

num2=Reading the number from the right, after the first one's digit, how many two's are there?
num1=Reading from the right, how many one's are there?

answer is the lesser of num1, num2. This is an hypothesis, and untested.

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