Cookies For Me

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

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

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

It states that there are leftovers

Razzi Masroor - 4 years, 2 months ago

Log in to reply

I modified my solution to match the modified problem.

Richard Costen - 4 years, 2 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...