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.

Question

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.

Reiny · Answer

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

Steve · Answer

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