In 2011, the estimated population of Canada was 34 699 000. If the government wants to use an alphabetic string using letters of the alphabet for every person in Canada. How long should the string of letters (repetition allowed) be so that every person in Canada can have a unique code?
would 4 letters be enough?
26^4 = 459976 , no
how about 5 letters ?
26^5 = 11,881,376 , not enough
26^6 = 308,915,776
That will do it.
The string must be 6 letters long
To determine the length of the string of letters needed to assign a unique code to every person in Canada, we need to calculate the number of possible combinations.
There are 26 letters in the English alphabet (assuming we are using only uppercase letters). Since repetition is allowed, each letter can be chosen from the 26 available options.
The formula to calculate the number of possible combinations is:
Number of Combinations = Number of Options ^ Length of the String
In this case, the number of options is 26 (the number of letters in the alphabet). We need to find the length of the string that would allow for 34,699,000 different codes.
Using the formula, we can solve for the length of the string:
34,699,000 = 26 ^ Length of the String
Taking the logarithm of both sides (base 26), we can solve for the length of the string:
log base 26 (34,699,000) = Length of the String
Using a scientific calculator or an online logarithm calculator, we can find that the length of the string should be approximately 5.528.
Since we cannot have fractional lengths, we need to round up to the nearest whole number. Therefore, the string of letters should be at least 6 characters long to provide a unique code for every person in Canada.
To determine the length of the string of letters required for every person in Canada to have a unique code, we need to consider the number of possible combinations.
There are 26 letters in the English alphabet (assuming we're using the English alphabet for the string of letters). Since repetition is allowed, there are 26 options for each position in the string.
The total number of possible combinations can be calculated using the formula:
Total number of combinations = Number of options for each position ^ Length of the string
In this case, the number of options for each position is 26, and we want the total number of combinations to be equal to or greater than the estimated population of Canada, which is 34,699,000.
Let's solve for the length of the string:
26^x >= 34,699,000
To solve this equation, we can take the logarithm of both sides:
log(26^x) >= log(34,699,000)
x * log(26) >= log(34,699,000)
Now, divide both sides of the equation by log(26) to solve for x:
x >= log(34,699,000) / log(26)
x >= 6.672
Since we can't have a fraction of a letter, we need to round up to the nearest whole number. Therefore, the length of the string of letters should be at least 7 to ensure every person in Canada can have a unique code.