Cookies For Me

Number Theory Level 2

Cookie Monster's mum bakes cookies in batches of 15 for the entire family.
Cookie Monster eats 9 cookies every time, but only if there are at least 9 left.
Cookie Monster's younger sister eats cookies 1 at a time, after Cookie monster is done with them.

After a day of baking, Cookie Monster's mum sees that there are no cookies left. Given that the younger sister ate at least 1 cookie, what is the minimum possible number of cookies that she ate?

1 2 4 3

2 solutions

Greg Grapsas
Mar 18, 2017

Tho i got it right the correct answer is 0. If she makes 3 batches he will ultimately eat 45..leaving 0. Otherwise this problem is worded very poorly.

Although I agree the question could be worded better, I think the answer is 3. It cannot be zero, because if it was, then cookies would not be left over.

Lohith Tummala - 4 years, 2 months ago

Adding "Of these possibilities, " or "If there are cookies left over, " is sufficient to fix the problem.

Gregory Lewis - 4 years, 2 months ago

A remainder of 3 means she made 30 cookies and 3*9 or 27 were eaten. But if she made 45 cookies then all 45 would be eaten eventually.

Greg Grapsas - 4 years, 2 months ago

Richard Costen
Mar 19, 2017

If $m,n$ are positive integers, then the remaining cookies (eaten by the younger sister) can be expressed as $15n-9m=3(5n-3m)$ . Thus the remainder is a multiple of 3, such as 0 ( if $n=3,m=5$ ), or 3 ( if $n=2,m=3$ ). Since she ate at least one cookie, the smallest is $\boxed{3}$

It states that there are leftovers

Razzi Masroor - 4 years, 2 months ago

I modified my solution to match the modified problem.

Richard Costen - 4 years, 2 months ago

Cookies For Me

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