I need to find the answer to this brain teaser. Mcnisens sells mcnuggets in packages of seven, eleven, or thirty. What is the largest number of pieces that yoh cannot order from mcnisens. I need it as a keyword for a playfair cipher. I have tried forty nine by adding them together but it didn't work.
The LCM of 7,11, and 30 = 7*11*30 = 2310
So 2311 would not divide by any of those, in each case there would be a remainder of 1
I think the question is poorly posed. Surely there is no largest number which is not divisible by 7,11 or 30.
Just take any huge product of powers of those numbers and add 1, such as 7^3 11^5 30^4 + 1
To find the largest number of pieces that you cannot order from McNisens, you can use a concept known as the "McNugget problem." This problem is a classic mathematical problem related to the Frobenius coin problem.
In this case, you need to determine the largest number that cannot be obtained by adding a combination of sevens, elevens, and thirties together.
To solve it, you can use a technique called "the Chicken McNugget Theorem." According to the theorem, the largest number you cannot obtain by combining two numbers (in this case, seven and eleven) is equal to the product of those two numbers minus their sum (7 x 11 - 7 - 11 = 59).
Now, to add the third number, which is thirty, you'll need to iterate through all possible combinations of sevens and elevens. By doing so, you can determine if any number less than thirty can't be obtained.
Here's a step-by-step approach to finding the largest number that cannot be obtained:
1. Start with the number thirty and subtract each combination of sevens and elevens that sum up to thirty or less.
30 - 7 = 23 (remaining combinations: 11)
30 - 11 = 19 (remaining combinations: 7)
2. Continue this process with the remaining combinations and subtract thirties.
19 - 7 = 12 (remaining combinations: 11, 7)
19 - 11 = 8 (remaining combinations: 7)
3. Repeat this process until you reach the smallest combination of sevens and elevens.
8 - 7 = 1 (remaining combinations: 11, 7)
At this point, you've reached the smallest combination of sevens and elevens. The largest number that cannot be obtained by combining sevens, elevens, and thirties is 1.
Therefore, the keyword for your Playfair cipher would be "1".