I bake

[BMAD]

Everyday I make the same number of cookies. On Monday, five people came over for cookies. I gave each of them the same amount and kept one for me. The next day, I baked the same amount but this time  eleven people came over. I gave them all an equal share and kept one for me. On the third day, I baked the same amount of cookies as the other days,  gave thirty-five people the same amount, and of course kept one for me. What are the three possible lowest amounts of batches I made each day? 

[Thalia]

If 385 is the LCM, I would assume you could just double it and add 1. So after 1 and 386, 771?

 

[gavinksong]

Once again, I'm not sure I understood the question correctly (sorry).

I think you're asking for three numbers, but I only have one. It's in the spoiler.

Spoiler

386 cookies

On Monday, you gave each person 77 cookies and kept one for yourself.

On Tuesday, you gave each person 35 cookies and kept one for yourself.

On Wednesday, you gave each person 11 cookies and kept one for yourself.

 

[BMAD]

You understood it correctly. You have one of the numbers but there are actually more that meet the requirements. I just want the lowest answers. 

[gavinksong]

OH, haha. Is one of the answers...

Spoiler

one?

 

[BMAD]

9 minutes ago, gavinksong said:

OH, haha. Is one of the answers...

  Hide contents

one?

 

Yup. One more answer

[Donald Cartmill]

I am with gavinksong...there is only one answer  which is the lowest common denominator for the three groups (plus 1)

[gavinksong]

1 hour ago, Donald Cartmill said:

I am with gavinksong...there is only one answer  which is the lowest common denominator for the three groups (plus 1)

Perhaps... but sometimes there is more than meets the eye, my friend.

I shall put forth another guess.

Spoiler

36 cookies.

On Monday, you gave each person seven cookies and kept one for yourself.

On Tuesday, you gave each person the same number of cookies, kept one for yourself, and threw the rest away.

On Wednesday, you gave each person one cookie and kept one for yourself.

 

[BMAD]

Yes it follows this pattern:

1+5x7x11xN

Where N=0,1,2,3,4,5,...

This will ensure the remainder is always one. 

Edited August 12, 2017 by BMAD

[gavinksong]

Wow, I feel pretty stupid. 

You were literally asking for the three lowest solutions. I don't know what I was thinking.