How many cookies does someone need to grab to be certain to obtain a flavor?
$begingroup$
I often found this riddle in many exams but I got often confused on how to tackle it. While it involves maths. I wonder if there is a subtle or a more layman method to obtain an answer using common sense?.
The problem which I'm about to describe isn't a specific homework problem. Is just a situation which I had imagined just now based on the kind of situation which often gets me confused. Okay here it goes:
A toddler want to grab some strawberry cookies. However there are
three flavors of those cookies in a jar, which just happen to be atop
of a refrigerator. There is a ladder in the kitchen, but the height of
that ladder isn't bigger enough for him to tell the difference between
which flavor of the cookies is which, all he can do is extend his arm
and take out the cookies from the jar. The child knows from his mom
that she made 10 of those strawberry cookies in the morning. However
he knows that the jar also has leftovers which he spotted on the night
before and these were 6 of vanilla flavor and 5 of chocolate chips.
Okay now comes the part where I often got stuck at:
What is the least amount of cookies that he has to take out from the jar to be certain that he has 4 of chocolate chips, 5 of vanilla and 7 of of strawberries?.
Now a second question
What is the least amount that he has to take out to be certain that he has all the strawberries and all chocolate chips?
And finally the third one
What is the least amount that he has to take from the jar to be certain that he has 1 of each flavor.
What I do remember from this situation is that when solving this riddle you often consider the most difficult scenario, in other words. He needs to take out let's say 10 in this case so with that he is certain that has strawberries. However I'm not very sure if this reasoning is valid.
Can somebody give me some help with this?
I'm slow at catching up ideas so, I'd like the answer could show or include the most details as possible and explain why certain decision or argument is taken.
riddle probability word-problem
asked yesterday
Chris Steinbeck BellChris Steinbeck Bell
1514
$endgroup$
add a comment |
$begingroup$
I often found this riddle in many exams but I got often confused on how to tackle it. While it involves maths. I wonder if there is a subtle or a more layman method to obtain an answer using common sense?.
The problem which I'm about to describe isn't a specific homework problem. Is just a situation which I had imagined just now based on the kind of situation which often gets me confused. Okay here it goes:
A toddler want to grab some strawberry cookies. However there are
three flavors of those cookies in a jar, which just happen to be atop
of a refrigerator. There is a ladder in the kitchen, but the height of
that ladder isn't bigger enough for him to tell the difference between
which flavor of the cookies is which, all he can do is extend his arm
and take out the cookies from the jar. The child knows from his mom
that she made 10 of those strawberry cookies in the morning. However
he knows that the jar also has leftovers which he spotted on the night
before and these were 6 of vanilla flavor and 5 of chocolate chips.
Okay now comes the part where I often got stuck at:
What is the least amount of cookies that he has to take out from the jar to be certain that he has 4 of chocolate chips, 5 of vanilla and 7 of of strawberries?.
Now a second question
What is the least amount that he has to take out to be certain that he has all the strawberries and all chocolate chips?
And finally the third one
What is the least amount that he has to take from the jar to be certain that he has 1 of each flavor.
What I do remember from this situation is that when solving this riddle you often consider the most difficult scenario, in other words. He needs to take out let's say 10 in this case so with that he is certain that has strawberries. However I'm not very sure if this reasoning is valid.
Can somebody give me some help with this?
I'm slow at catching up ideas so, I'd like the answer could show or include the most details as possible and explain why certain decision or argument is taken.
riddle probability word-problem
asked yesterday
Chris Steinbeck BellChris Steinbeck Bell
1514
$endgroup$
5
$begingroup$
Okay, a few things. 1: if the cookies were made this morning, they are very likely on top of the other cookies within the jar, so the selection should be trivial. 2: Since when do toddlers take less than all of the cookies?
$endgroup$
– Ian MacDonald
yesterday
add a comment |
$begingroup$
I often found this riddle in many exams but I got often confused on how to tackle it. While it involves maths. I wonder if there is a subtle or a more layman method to obtain an answer using common sense?.
The problem which I'm about to describe isn't a specific homework problem. Is just a situation which I had imagined just now based on the kind of situation which often gets me confused. Okay here it goes:
A toddler want to grab some strawberry cookies. However there are
three flavors of those cookies in a jar, which just happen to be atop
of a refrigerator. There is a ladder in the kitchen, but the height of
that ladder isn't bigger enough for him to tell the difference between
which flavor of the cookies is which, all he can do is extend his arm
and take out the cookies from the jar. The child knows from his mom
that she made 10 of those strawberry cookies in the morning. However
he knows that the jar also has leftovers which he spotted on the night
before and these were 6 of vanilla flavor and 5 of chocolate chips.
Okay now comes the part where I often got stuck at:
What is the least amount of cookies that he has to take out from the jar to be certain that he has 4 of chocolate chips, 5 of vanilla and 7 of of strawberries?.
Now a second question
What is the least amount that he has to take out to be certain that he has all the strawberries and all chocolate chips?
And finally the third one
What is the least amount that he has to take from the jar to be certain that he has 1 of each flavor.
What I do remember from this situation is that when solving this riddle you often consider the most difficult scenario, in other words. He needs to take out let's say 10 in this case so with that he is certain that has strawberries. However I'm not very sure if this reasoning is valid.
Can somebody give me some help with this?
I'm slow at catching up ideas so, I'd like the answer could show or include the most details as possible and explain why certain decision or argument is taken.
riddle probability word-problem
asked yesterday
Chris Steinbeck BellChris Steinbeck Bell
1514
$endgroup$
I often found this riddle in many exams but I got often confused on how to tackle it. While it involves maths. I wonder if there is a subtle or a more layman method to obtain an answer using common sense?.
The problem which I'm about to describe isn't a specific homework problem. Is just a situation which I had imagined just now based on the kind of situation which often gets me confused. Okay here it goes:
A toddler want to grab some strawberry cookies. However there are
three flavors of those cookies in a jar, which just happen to be atop
of a refrigerator. There is a ladder in the kitchen, but the height of
that ladder isn't bigger enough for him to tell the difference between
which flavor of the cookies is which, all he can do is extend his arm
and take out the cookies from the jar. The child knows from his mom
that she made 10 of those strawberry cookies in the morning. However
he knows that the jar also has leftovers which he spotted on the night
before and these were 6 of vanilla flavor and 5 of chocolate chips.
Okay now comes the part where I often got stuck at:
What is the least amount of cookies that he has to take out from the jar to be certain that he has 4 of chocolate chips, 5 of vanilla and 7 of of strawberries?.
Now a second question
What is the least amount that he has to take out to be certain that he has all the strawberries and all chocolate chips?
And finally the third one
What is the least amount that he has to take from the jar to be certain that he has 1 of each flavor.
What I do remember from this situation is that when solving this riddle you often consider the most difficult scenario, in other words. He needs to take out let's say 10 in this case so with that he is certain that has strawberries. However I'm not very sure if this reasoning is valid.
Can somebody give me some help with this?
I'm slow at catching up ideas so, I'd like the answer could show or include the most details as possible and explain why certain decision or argument is taken.
riddle probability word-problem
riddle probability word-problem
asked yesterday
Chris Steinbeck BellChris Steinbeck Bell
1514
asked yesterday
Chris Steinbeck BellChris Steinbeck Bell
1514
asked yesterday
Chris Steinbeck BellChris Steinbeck Bell
1514
asked yesterday
Chris Steinbeck BellChris Steinbeck Bell
1514
asked yesterday
Chris Steinbeck BellChris Steinbeck Bell
1514
1514
5
$begingroup$
Okay, a few things. 1: if the cookies were made this morning, they are very likely on top of the other cookies within the jar, so the selection should be trivial. 2: Since when do toddlers take less than all of the cookies?
$endgroup$
– Ian MacDonald
yesterday
add a comment |
5
$begingroup$
Okay, a few things. 1: if the cookies were made this morning, they are very likely on top of the other cookies within the jar, so the selection should be trivial. 2: Since when do toddlers take less than all of the cookies?
$endgroup$
– Ian MacDonald
yesterday
5
5
$begingroup$
Okay, a few things. 1: if the cookies were made this morning, they are very likely on top of the other cookies within the jar, so the selection should be trivial. 2: Since when do toddlers take less than all of the cookies?
$endgroup$
– Ian MacDonald
yesterday
$begingroup$
Okay, a few things. 1: if the cookies were made this morning, they are very likely on top of the other cookies within the jar, so the selection should be trivial. 2: Since when do toddlers take less than all of the cookies?
$endgroup$
– Ian MacDonald
yesterday
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Originally there are;
10 S, 6 V and 5C
For the first case where he wants to have 7 S, 5 V and , 4 C. (so we dont want to have 3S, 1V and 1C)
In the worst case scenario;
we need to think that he is very unlucky, while taking out cookies, he takes all strawberries first, where there are 10 of them, so extra 3 cookies, and etc.
so
He has to take out 10S+6V+4C = 20 cookies to guarantee he can have 7S, 5V and 4C. Put the extras back later.
I do not want to continue for the rest since the same methodology works for them too:
in the worst case scenario, take out first the type of cookie which has the most extras (number of cookies available - wanted amount of cookies), then second most and lastly the least one.
This will give you the number of cookies to guarantee to have some specific number of cookies.
answered yesterday
OrayOray
16.1k437157
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
Originally there are;
10 S, 6 V and 5C
For the first case where he wants to have 7 S, 5 V and , 4 C. (so we dont want to have 3S, 1V and 1C)
In the worst case scenario;
we need to think that he is very unlucky, while taking out cookies, he takes all strawberries first, where there are 10 of them, so extra 3 cookies, and etc.
so
He has to take out 10S+6V+4C = 20 cookies to guarantee he can have 7S, 5V and 4C. Put the extras back later.
I do not want to continue for the rest since the same methodology works for them too:
in the worst case scenario, take out first the type of cookie which has the most extras (number of cookies available - wanted amount of cookies), then second most and lastly the least one.
This will give you the number of cookies to guarantee to have some specific number of cookies.
answered yesterday
OrayOray
16.1k437157
$endgroup$
add a comment |
$begingroup$
Originally there are;
10 S, 6 V and 5C
For the first case where he wants to have 7 S, 5 V and , 4 C. (so we dont want to have 3S, 1V and 1C)
In the worst case scenario;
we need to think that he is very unlucky, while taking out cookies, he takes all strawberries first, where there are 10 of them, so extra 3 cookies, and etc.
so
He has to take out 10S+6V+4C = 20 cookies to guarantee he can have 7S, 5V and 4C. Put the extras back later.
I do not want to continue for the rest since the same methodology works for them too:
in the worst case scenario, take out first the type of cookie which has the most extras (number of cookies available - wanted amount of cookies), then second most and lastly the least one.
This will give you the number of cookies to guarantee to have some specific number of cookies.
answered yesterday
OrayOray
16.1k437157
$endgroup$
add a comment |
$begingroup$
Originally there are;
10 S, 6 V and 5C
For the first case where he wants to have 7 S, 5 V and , 4 C. (so we dont want to have 3S, 1V and 1C)
In the worst case scenario;
we need to think that he is very unlucky, while taking out cookies, he takes all strawberries first, where there are 10 of them, so extra 3 cookies, and etc.
so
He has to take out 10S+6V+4C = 20 cookies to guarantee he can have 7S, 5V and 4C. Put the extras back later.
I do not want to continue for the rest since the same methodology works for them too:
in the worst case scenario, take out first the type of cookie which has the most extras (number of cookies available - wanted amount of cookies), then second most and lastly the least one.
This will give you the number of cookies to guarantee to have some specific number of cookies.
answered yesterday
OrayOray
16.1k437157
$endgroup$
Originally there are;
10 S, 6 V and 5C
For the first case where he wants to have 7 S, 5 V and , 4 C. (so we dont want to have 3S, 1V and 1C)
In the worst case scenario;
we need to think that he is very unlucky, while taking out cookies, he takes all strawberries first, where there are 10 of them, so extra 3 cookies, and etc.
so
He has to take out 10S+6V+4C = 20 cookies to guarantee he can have 7S, 5V and 4C. Put the extras back later.
I do not want to continue for the rest since the same methodology works for them too:
in the worst case scenario, take out first the type of cookie which has the most extras (number of cookies available - wanted amount of cookies), then second most and lastly the least one.
This will give you the number of cookies to guarantee to have some specific number of cookies.
answered yesterday
OrayOray
16.1k437157
edited yesterday
answered yesterday
OrayOray
16.1k437157
answered yesterday
OrayOray
16.1k437157
answered yesterday
OrayOray
16.1k437157
16.1k437157
add a comment |
add a comment |
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5
$begingroup$
Okay, a few things. 1: if the cookies were made this morning, they are very likely on top of the other cookies within the jar, so the selection should be trivial. 2: Since when do toddlers take less than all of the cookies?
$endgroup$
– Ian MacDonald
yesterday