What is the largest number possible that isn't some combination of 4 and 7?

The answer is 17 (I'm fairly certain of this) but I can't write an equation for it. This is 5th grade math, so it shouldn't be that hard... but I haven't done math in 20+ years.

So, can someone give me an equation or other mathematical explanation?

Thanks.

I'm not sure how to ask the question differently. The way it was posed to the students was something like "if you have 4 packs of nuggets and 7 packs of nuggets, what is the largest number that some combination of 4 and 7 dont divide into."

So, if you picked 33, you would say that 3 4-packs and 3 7-packs make 33.

Basically, what is the largest number that some multiple of 7 and 4 dont add up to.

Actually, I would ask JTokash.

If the question is clear, he will calculate the answer and then lay it all out for you in such a simple, clear fashion that you will understand both how any formula is derived and how he determined the answer.

(Justin, if you see this, know that you and Liz are still in my mind. Hope life is sweet and wonderful for both of you!)

Frobenius (coin) problem

Formula when you're only dealing with 2 numbers

(x-1)(y-1)-1

or

xy-x-y

So yes, 17 is the correct answer. You can google the why if you want more info, it's time for bed.

There is an alternate formula for dealing with 3 different numbers. No known formula for 4 or more IIRC.

I didn't change either of my posts, so I'm not sure what was wrong with them, but your formulas appear to be correct. Thank you. I passed them on to my sister and her husband so they could pass it on to their son.

I love this place.

Thornton Melon: The answer is... [the answer hits him] ... 4?

and in that case, the answer is 42!

So long, and thanks for all the fish!!

🍺