(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Chicken nuggets are only sold in baskets of either 7 or 11 nuggets. What is the largest

number of nuggets that is impossible to order exactly? You must prove that your answer

is correct.

2. Relevant equations

Not sure what equations could be used, but I guess 7(x1) + 11(x2) = (A) is what we're technically trying to solve and we're trying to get a number (A) that can't be achieved when you plug in any combinations of whole numbers for (x1) and (x2)

ex:

if (A)=43, a solution could be (x1)=3 and (x2)=2

if (A)= 23, there can be no combinations of (x1) and (x2) that will fulfill the equation

What I need to find is the largest (A) where there will be no combinations, and i've been able to find some like 52, 59, 94, but I can't seem to find the largest one because I keep finding more and more.

3. The attempt at a solution

I'm not sure how to approach this... it's been the first week of my linear algebra course and we've learned some things on matrices but I'm not sure how I could apply it to this problem. I've written out so many combinations of the sums of multiples of 7's and 11's and I am just stumped. I can find values of (A) where there can't be any whole numbers for (x1) and (x2), but how can I be sure that it's the largest amount?

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# Homework Help: Linear Algebra (Abstract impossible combination question)

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