Mixing
Cupcake division
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up vote
3
down vote
favorite
A elementary school student brought cupcakes to their class to celebrate their birthday! However, there's a problem: There are 25 students in the classroom, and only 24 cupcakes!
The students have recently been studying fractions. One of the students quickly puts forth a solution: "Everybody can have 24/25 of a cupcake! We can cut 1/25 off of every cupcake, combine those into one cupcake, and then we'll have 25." However, nobody seems willing to accept a "cupcake" made out of 24 cupcake crumbs.
It is up to you to figure out how to divide the cupcakes in a way that is both fair, and doesn't reduce the treats to pastry dust. What strategy can you use to ensure that the smallest slice you have to make is as large as possible?
This puzzle is purely mathematical: Every student must get exactly 24/25 of a cupcake, every cupcake is exactly the same size, the students will wait patiently while you measure and cut the cakes, etc..
This puzzle was inspired by a page from Math Curse, where the main character faces a similar situation. They resolve it by simply not eating a cupcake, but here you have no such option...
This is my first post on PuzzlingSE, so please tell me if I'm doing anything wrong!
mathematics optimization
asked 3 hours ago
Woofmao
164
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Woofmao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
3
down vote
favorite
A elementary school student brought cupcakes to their class to celebrate their birthday! However, there's a problem: There are 25 students in the classroom, and only 24 cupcakes!
The students have recently been studying fractions. One of the students quickly puts forth a solution: "Everybody can have 24/25 of a cupcake! We can cut 1/25 off of every cupcake, combine those into one cupcake, and then we'll have 25." However, nobody seems willing to accept a "cupcake" made out of 24 cupcake crumbs.
It is up to you to figure out how to divide the cupcakes in a way that is both fair, and doesn't reduce the treats to pastry dust. What strategy can you use to ensure that the smallest slice you have to make is as large as possible?
This puzzle is purely mathematical: Every student must get exactly 24/25 of a cupcake, every cupcake is exactly the same size, the students will wait patiently while you measure and cut the cakes, etc..
This puzzle was inspired by a page from Math Curse, where the main character faces a similar situation. They resolve it by simply not eating a cupcake, but here you have no such option...
This is my first post on PuzzlingSE, so please tell me if I'm doing anything wrong!
mathematics optimization
asked 3 hours ago
Woofmao
164
New contributor
Woofmao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
If I cut every cupcake into twenty-five pieces, then give each student a 1/25th from each cupcake, then every student gets a "cupcake" made out of 24 cupcake crumbs! All fair! Nobody can complain :)
– Hugh
1 hour ago
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
A elementary school student brought cupcakes to their class to celebrate their birthday! However, there's a problem: There are 25 students in the classroom, and only 24 cupcakes!
The students have recently been studying fractions. One of the students quickly puts forth a solution: "Everybody can have 24/25 of a cupcake! We can cut 1/25 off of every cupcake, combine those into one cupcake, and then we'll have 25." However, nobody seems willing to accept a "cupcake" made out of 24 cupcake crumbs.
It is up to you to figure out how to divide the cupcakes in a way that is both fair, and doesn't reduce the treats to pastry dust. What strategy can you use to ensure that the smallest slice you have to make is as large as possible?
This puzzle is purely mathematical: Every student must get exactly 24/25 of a cupcake, every cupcake is exactly the same size, the students will wait patiently while you measure and cut the cakes, etc..
This puzzle was inspired by a page from Math Curse, where the main character faces a similar situation. They resolve it by simply not eating a cupcake, but here you have no such option...
This is my first post on PuzzlingSE, so please tell me if I'm doing anything wrong!
mathematics optimization
asked 3 hours ago
Woofmao
164
New contributor
Woofmao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
A elementary school student brought cupcakes to their class to celebrate their birthday! However, there's a problem: There are 25 students in the classroom, and only 24 cupcakes!
The students have recently been studying fractions. One of the students quickly puts forth a solution: "Everybody can have 24/25 of a cupcake! We can cut 1/25 off of every cupcake, combine those into one cupcake, and then we'll have 25." However, nobody seems willing to accept a "cupcake" made out of 24 cupcake crumbs.
It is up to you to figure out how to divide the cupcakes in a way that is both fair, and doesn't reduce the treats to pastry dust. What strategy can you use to ensure that the smallest slice you have to make is as large as possible?
This puzzle is purely mathematical: Every student must get exactly 24/25 of a cupcake, every cupcake is exactly the same size, the students will wait patiently while you measure and cut the cakes, etc..
This puzzle was inspired by a page from Math Curse, where the main character faces a similar situation. They resolve it by simply not eating a cupcake, but here you have no such option...
This is my first post on PuzzlingSE, so please tell me if I'm doing anything wrong!
mathematics optimization
mathematics optimization
asked 3 hours ago
Woofmao
164
New contributor
Woofmao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 3 hours ago
Woofmao
164
New contributor
Woofmao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 hours ago
asked 3 hours ago
Woofmao
164
New contributor
Woofmao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 3 hours ago
Woofmao
164
asked 3 hours ago
Woofmao
164
164
New contributor
Woofmao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Woofmao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Woofmao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
If I cut every cupcake into twenty-five pieces, then give each student a 1/25th from each cupcake, then every student gets a "cupcake" made out of 24 cupcake crumbs! All fair! Nobody can complain :)
– Hugh
1 hour ago
add a comment |Â
1
If I cut every cupcake into twenty-five pieces, then give each student a 1/25th from each cupcake, then every student gets a "cupcake" made out of 24 cupcake crumbs! All fair! Nobody can complain :)
– Hugh
1 hour ago
1
1
If I cut every cupcake into twenty-five pieces, then give each student a 1/25th from each cupcake, then every student gets a "cupcake" made out of 24 cupcake crumbs! All fair! Nobody can complain :)
– Hugh
1 hour ago
If I cut every cupcake into twenty-five pieces, then give each student a 1/25th from each cupcake, then every student gets a "cupcake" made out of 24 cupcake crumbs! All fair! Nobody can complain :)
– Hugh
1 hour ago
add a comment |Â
3 Answers
3
active
oldest
votes
up vote
2
down vote
My smallest piece is
$frac625$
You split the cakes as follows:
$3$ cakes as $frac625+frac625+frac625+frac725$
$13$ cakes as $frac725+frac925+frac925$
$8$ cakes as $frac825+frac825+frac925$
This gives $9$, $16$, $16$, and $34$ pieces of sizes $frac625$ to $frac925$.
Then put them together as
$9$ cakes of $frac625+frac925+frac925$
$16$ cakes of $frac725+frac825+frac925$
answered 14 mins ago
Jaap Scherphuis
13.2k12260
add a comment |Â
up vote
0
down vote
How about
- Cut 19 cupcakes into five fifths each. You have 95 fifths.
- Take one fifth out of each of the other 5 cupcakes. You have 100 fifths and 5 leftovers.
- Give each student 4 fifths.
- Cut the 5 leftovers each into 5 equal pieces. Give each student 1.
Each student got the same number of the same sized bits, so it must be fair.
The smallest piece is
The fifth of the leftover, which would be 4/25 (16%) of a cupcake.
answered 44 mins ago
deep thought
1,414321
it seems your answer is the same as mine :) I noticed your late sorry...
– Oray
35 mins ago
1
@Oray it's okay, we'll just divide most of our upvotes into fifths, etc etc
– deep thought
31 mins ago
add a comment |Â
up vote
0
down vote
Let's call a whole cupcake
100 unit and what we are aiming is 96 dividing these 100s into pieces
so the obvious answer from the question was
$4$
so I take
9 of $100$ unit into $5$ of 20 unit pieces which makes $45$ pieces of 20 units.
and secondly
15 of $100$ unit into $2$ of 32 unit pieces and $1$ of 36 unit pieces which makes $30$ of 32 unit pieces and $15$ of $36 unit pieces.
as a table
So from now on, I form our cakes as below:
We do this procedure
$4$ times more and we will not have any cake leftover.
so the answer becomes
$frac525$
answered 49 mins ago
Oray
15.3k435147
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
My smallest piece is
$frac625$
You split the cakes as follows:
$3$ cakes as $frac625+frac625+frac625+frac725$
$13$ cakes as $frac725+frac925+frac925$
$8$ cakes as $frac825+frac825+frac925$
This gives $9$, $16$, $16$, and $34$ pieces of sizes $frac625$ to $frac925$.
Then put them together as
$9$ cakes of $frac625+frac925+frac925$
$16$ cakes of $frac725+frac825+frac925$
answered 14 mins ago
Jaap Scherphuis
13.2k12260
add a comment |Â
up vote
2
down vote
My smallest piece is
$frac625$
You split the cakes as follows:
$3$ cakes as $frac625+frac625+frac625+frac725$
$13$ cakes as $frac725+frac925+frac925$
$8$ cakes as $frac825+frac825+frac925$
This gives $9$, $16$, $16$, and $34$ pieces of sizes $frac625$ to $frac925$.
Then put them together as
$9$ cakes of $frac625+frac925+frac925$
$16$ cakes of $frac725+frac825+frac925$
answered 14 mins ago
Jaap Scherphuis
13.2k12260
add a comment |Â
up vote
2
down vote
up vote
2
down vote
My smallest piece is
$frac625$
You split the cakes as follows:
$3$ cakes as $frac625+frac625+frac625+frac725$
$13$ cakes as $frac725+frac925+frac925$
$8$ cakes as $frac825+frac825+frac925$
This gives $9$, $16$, $16$, and $34$ pieces of sizes $frac625$ to $frac925$.
Then put them together as
$9$ cakes of $frac625+frac925+frac925$
$16$ cakes of $frac725+frac825+frac925$
answered 14 mins ago
Jaap Scherphuis
13.2k12260
My smallest piece is
$frac625$
You split the cakes as follows:
$3$ cakes as $frac625+frac625+frac625+frac725$
$13$ cakes as $frac725+frac925+frac925$
$8$ cakes as $frac825+frac825+frac925$
This gives $9$, $16$, $16$, and $34$ pieces of sizes $frac625$ to $frac925$.
Then put them together as
$9$ cakes of $frac625+frac925+frac925$
$16$ cakes of $frac725+frac825+frac925$
answered 14 mins ago
Jaap Scherphuis
13.2k12260
answered 14 mins ago
Jaap Scherphuis
13.2k12260
answered 14 mins ago
Jaap Scherphuis
13.2k12260
answered 14 mins ago
Jaap Scherphuis
13.2k12260
13.2k12260
add a comment |Â
add a comment |Â
up vote
0
down vote
How about
- Cut 19 cupcakes into five fifths each. You have 95 fifths.
- Take one fifth out of each of the other 5 cupcakes. You have 100 fifths and 5 leftovers.
- Give each student 4 fifths.
- Cut the 5 leftovers each into 5 equal pieces. Give each student 1.
Each student got the same number of the same sized bits, so it must be fair.
The smallest piece is
The fifth of the leftover, which would be 4/25 (16%) of a cupcake.
answered 44 mins ago
deep thought
1,414321
it seems your answer is the same as mine :) I noticed your late sorry...
– Oray
35 mins ago
1
@Oray it's okay, we'll just divide most of our upvotes into fifths, etc etc
– deep thought
31 mins ago
add a comment |Â
up vote
0
down vote
How about
- Cut 19 cupcakes into five fifths each. You have 95 fifths.
- Take one fifth out of each of the other 5 cupcakes. You have 100 fifths and 5 leftovers.
- Give each student 4 fifths.
- Cut the 5 leftovers each into 5 equal pieces. Give each student 1.
Each student got the same number of the same sized bits, so it must be fair.
The smallest piece is
The fifth of the leftover, which would be 4/25 (16%) of a cupcake.
answered 44 mins ago
deep thought
1,414321
it seems your answer is the same as mine :) I noticed your late sorry...
– Oray
35 mins ago
1
@Oray it's okay, we'll just divide most of our upvotes into fifths, etc etc
– deep thought
31 mins ago
add a comment |Â
up vote
0
down vote
up vote
0
down vote
How about
- Cut 19 cupcakes into five fifths each. You have 95 fifths.
- Take one fifth out of each of the other 5 cupcakes. You have 100 fifths and 5 leftovers.
- Give each student 4 fifths.
- Cut the 5 leftovers each into 5 equal pieces. Give each student 1.
Each student got the same number of the same sized bits, so it must be fair.
The smallest piece is
The fifth of the leftover, which would be 4/25 (16%) of a cupcake.
answered 44 mins ago
deep thought
1,414321
How about
- Cut 19 cupcakes into five fifths each. You have 95 fifths.
- Take one fifth out of each of the other 5 cupcakes. You have 100 fifths and 5 leftovers.
- Give each student 4 fifths.
- Cut the 5 leftovers each into 5 equal pieces. Give each student 1.
Each student got the same number of the same sized bits, so it must be fair.
The smallest piece is
The fifth of the leftover, which would be 4/25 (16%) of a cupcake.
answered 44 mins ago
deep thought
1,414321
answered 44 mins ago
deep thought
1,414321
answered 44 mins ago
deep thought
1,414321
answered 44 mins ago
deep thought
1,414321
1,414321
it seems your answer is the same as mine :) I noticed your late sorry...
– Oray
35 mins ago
1
@Oray it's okay, we'll just divide most of our upvotes into fifths, etc etc
– deep thought
31 mins ago
add a comment |Â
it seems your answer is the same as mine :) I noticed your late sorry...
– Oray
35 mins ago
1
@Oray it's okay, we'll just divide most of our upvotes into fifths, etc etc
– deep thought
31 mins ago
it seems your answer is the same as mine :) I noticed your late sorry...
– Oray
35 mins ago
it seems your answer is the same as mine :) I noticed your late sorry...
– Oray
35 mins ago
1
1
@Oray it's okay, we'll just divide most of our upvotes into fifths, etc etc
– deep thought
31 mins ago
@Oray it's okay, we'll just divide most of our upvotes into fifths, etc etc
– deep thought
31 mins ago
add a comment |Â
up vote
0
down vote
Let's call a whole cupcake
100 unit and what we are aiming is 96 dividing these 100s into pieces
so the obvious answer from the question was
$4$
so I take
9 of $100$ unit into $5$ of 20 unit pieces which makes $45$ pieces of 20 units.
and secondly
15 of $100$ unit into $2$ of 32 unit pieces and $1$ of 36 unit pieces which makes $30$ of 32 unit pieces and $15$ of $36 unit pieces.
as a table
So from now on, I form our cakes as below:
We do this procedure
$4$ times more and we will not have any cake leftover.
so the answer becomes
$frac525$
answered 49 mins ago
Oray
15.3k435147
add a comment |Â
up vote
0
down vote
Let's call a whole cupcake
100 unit and what we are aiming is 96 dividing these 100s into pieces
so the obvious answer from the question was
$4$
so I take
9 of $100$ unit into $5$ of 20 unit pieces which makes $45$ pieces of 20 units.
and secondly
15 of $100$ unit into $2$ of 32 unit pieces and $1$ of 36 unit pieces which makes $30$ of 32 unit pieces and $15$ of $36 unit pieces.
as a table
So from now on, I form our cakes as below:
We do this procedure
$4$ times more and we will not have any cake leftover.
so the answer becomes
$frac525$
answered 49 mins ago
Oray
15.3k435147
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Let's call a whole cupcake
100 unit and what we are aiming is 96 dividing these 100s into pieces
so the obvious answer from the question was
$4$
so I take
9 of $100$ unit into $5$ of 20 unit pieces which makes $45$ pieces of 20 units.
and secondly
15 of $100$ unit into $2$ of 32 unit pieces and $1$ of 36 unit pieces which makes $30$ of 32 unit pieces and $15$ of $36 unit pieces.
as a table
So from now on, I form our cakes as below:
We do this procedure
$4$ times more and we will not have any cake leftover.
so the answer becomes
$frac525$
answered 49 mins ago
Oray
15.3k435147
Let's call a whole cupcake
100 unit and what we are aiming is 96 dividing these 100s into pieces
so the obvious answer from the question was
$4$
so I take
9 of $100$ unit into $5$ of 20 unit pieces which makes $45$ pieces of 20 units.
and secondly
15 of $100$ unit into $2$ of 32 unit pieces and $1$ of 36 unit pieces which makes $30$ of 32 unit pieces and $15$ of $36 unit pieces.
as a table
So from now on, I form our cakes as below:
We do this procedure
$4$ times more and we will not have any cake leftover.
so the answer becomes
$frac525$
answered 49 mins ago
Oray
15.3k435147
edited 19 mins ago
answered 49 mins ago
Oray
15.3k435147
answered 49 mins ago
Oray
15.3k435147
answered 49 mins ago
Oray
15.3k435147
15.3k435147
add a comment |Â
add a comment |Â
Woofmao is a new contributor. Be nice, and check out our Code of Conduct.
Woofmao is a new contributor. Be nice, and check out our Code of Conduct.
Woofmao is a new contributor. Be nice, and check out our Code of Conduct.
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1
If I cut every cupcake into twenty-five pieces, then give each student a 1/25th from each cupcake, then every student gets a "cupcake" made out of 24 cupcake crumbs! All fair! Nobody can complain :)
– Hugh
1 hour ago