Mixing
Hard 4x8 chocolate bar Riddle v2
Clash Royale CLAN TAG#URR8PPP
up vote
2
down vote
favorite
This is inspired from this puzzle:
You have $4$x$8$ chocolate, you can cut only straight with the knife.
What is the least amount of cutting required to have $32$ pieces of 1x1 chocolates?
and
What if putting chocolates onto each other was not allowed?
logical-deduction
asked 51 mins ago
Oray
14.7k435142
add a comment |Â
up vote
2
down vote
favorite
This is inspired from this puzzle:
You have $4$x$8$ chocolate, you can cut only straight with the knife.
What is the least amount of cutting required to have $32$ pieces of 1x1 chocolates?
and
What if putting chocolates onto each other was not allowed?
logical-deduction
asked 51 mins ago
Oray
14.7k435142
Just to clarify, when you say least amount of cutting, does that mean the total length of all cuts?
– hexomino
40 mins ago
@hexomino total amount of cutting... not total length of cutting :)
– Oray
39 mins ago
My answer doesn't involve putting them on top of each other, but rearranging the cut pieces next to each other to achieve the same effect of cutting through multiple separate pieces in a single cutting action. Does this count?
– AHKieran
17 mins ago
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
This is inspired from this puzzle:
You have $4$x$8$ chocolate, you can cut only straight with the knife.
What is the least amount of cutting required to have $32$ pieces of 1x1 chocolates?
and
What if putting chocolates onto each other was not allowed?
logical-deduction
asked 51 mins ago
Oray
14.7k435142
This is inspired from this puzzle:
You have $4$x$8$ chocolate, you can cut only straight with the knife.
What is the least amount of cutting required to have $32$ pieces of 1x1 chocolates?
and
What if putting chocolates onto each other was not allowed?
logical-deduction
logical-deduction
asked 51 mins ago
Oray
14.7k435142
asked 51 mins ago
Oray
14.7k435142
edited 19 mins ago
asked 51 mins ago
Oray
14.7k435142
asked 51 mins ago
Oray
14.7k435142
asked 51 mins ago
Oray
14.7k435142
14.7k435142
Just to clarify, when you say least amount of cutting, does that mean the total length of all cuts?
– hexomino
40 mins ago
@hexomino total amount of cutting... not total length of cutting :)
– Oray
39 mins ago
My answer doesn't involve putting them on top of each other, but rearranging the cut pieces next to each other to achieve the same effect of cutting through multiple separate pieces in a single cutting action. Does this count?
– AHKieran
17 mins ago
add a comment |Â
Just to clarify, when you say least amount of cutting, does that mean the total length of all cuts?
– hexomino
40 mins ago
@hexomino total amount of cutting... not total length of cutting :)
– Oray
39 mins ago
My answer doesn't involve putting them on top of each other, but rearranging the cut pieces next to each other to achieve the same effect of cutting through multiple separate pieces in a single cutting action. Does this count?
– AHKieran
17 mins ago
Just to clarify, when you say least amount of cutting, does that mean the total length of all cuts?
– hexomino
40 mins ago
Just to clarify, when you say least amount of cutting, does that mean the total length of all cuts?
– hexomino
40 mins ago
@hexomino total amount of cutting... not total length of cutting :)
– Oray
39 mins ago
@hexomino total amount of cutting... not total length of cutting :)
– Oray
39 mins ago
My answer doesn't involve putting them on top of each other, but rearranging the cut pieces next to each other to achieve the same effect of cutting through multiple separate pieces in a single cutting action. Does this count?
– AHKieran
17 mins ago
My answer doesn't involve putting them on top of each other, but rearranging the cut pieces next to each other to achieve the same effect of cutting through multiple separate pieces in a single cutting action. Does this count?
– AHKieran
17 mins ago
add a comment |Â
5 Answers
5
active
oldest
votes
up vote
3
down vote
It can be done in
5 cuts.
because
Simply imagine repeatedly folding it in half like a piece of paper until it is $1times1$. Instead of folding, you cut and stack the pieces on top of each other. If you are not allowed to stack on top of each other for the cut, then you can put them next to each other instead.
$4times 8 = 2^2 times 2^3$ so it takes 5 cuts to reduce to $2^0 times 2^0$.
answered 25 mins ago
Jaap Scherphuis
12.5k12155
add a comment |Â
up vote
2
down vote
It may be done in
5 cuts if you are allowed to stack the pieces on top of each other after each cut.
Counting on this
First cut → two 4x4 pieces
Second cut → four 2x4 pieces
Third cut → eight 2x2 pieces
Fourth cut → sixteen 1x2 pieces
Fifth cut → thirty-two 1x1 squares
answered 25 mins ago
Tom
25.3k287148
add a comment |Â
up vote
1
down vote
Total Cuts:
5
Method:
Cut in half vertically, creating 2, 2x8 pieces, then place these end to end to get a 2x16 piece. Cut again vertically through both pieces, to get 4, 1x8 pieces. Place these side by side to form a 4x8 piece again, this time, cut in half horizontally, and move the pieces to form an 8x4 shape, cut and move into 16x2, then cut once more and you have 32 individual pieces. This totals 5 cuts.
Explanation:
This puzzle works because with each cut, we half the size of every piece. to work this out quickly, we could do log2(32) = 5.
answered 19 mins ago
AHKieran
1,106216
add a comment |Â
up vote
1
down vote
The answer is
31 times
Because
you can either cut rows of 8 (3 cuts, you now have 4 rows of 8), then separate each row with 7 cuts each. $3 + (4*7) = 31$.
or cut vertically first seven times to create 8 columns of 4, then cut each 3 times. $7 + (8*3) = 31$.
changing between cutting horizontally and vertically each time will not help getting a lower amount of cuts. it always results in 31.
Unless..
we are allowed to cut 4 rows, put them together as if the bar were still whole, and cut 7 times vertically. In that case we get 11 cuts. I don't think this is allowed in this puzzle
After Q-Edit:
In this puzzle, we don't have to separate the pieces and cut each piece on its own. As others now have said, it is possible with 5 cuts.
What if putting chocolates onto each other was not allowed?- You don't even have to stack the halves on top of each other, just arrange them next to each other so you can cut each piece the same way with one cut.
answered 36 mins ago
Cashbee
1,19015
1
There are other possibilities. e.g. cut into two 2x8, then those into 2x2s, etc.
– Jaap Scherphuis
35 mins ago
@JaapScherphuis see edit
– Cashbee
35 mins ago
@Cashbee there is no restriction in the question.
– Oray
32 mins ago
1
@Oray well yes there is. from the inspiration-puzzle:and every time we cut the chocolate we separate the pieces and cut each piece on its own. you did not say that this is not valid anymore for your puzzle. Anyway, I covered both possibilities
– Cashbee
30 mins ago
1
To be fair, you had that exact sentence in your own question when I read it. I see it is now removed. Well played
– Cashbee
24 mins ago
 |Â
show 1 more comment
up vote
0
down vote
0
because
Chocolate is usually already divided into
1 x 1blocks. You can easily crush it with your hand and you doesn't need any help of a knife.
I think that it is already divided into 32 blocks. Why would you provide dimensions4 x 8otherwise? Not2 x 4nor1 x 2?
answered 17 mins ago
mpasko256
99528
add a comment |Â
5 Answers
5
active
oldest
votes
5 Answers
5
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
It can be done in
5 cuts.
because
Simply imagine repeatedly folding it in half like a piece of paper until it is $1times1$. Instead of folding, you cut and stack the pieces on top of each other. If you are not allowed to stack on top of each other for the cut, then you can put them next to each other instead.
$4times 8 = 2^2 times 2^3$ so it takes 5 cuts to reduce to $2^0 times 2^0$.
answered 25 mins ago
Jaap Scherphuis
12.5k12155
add a comment |Â
up vote
3
down vote
It can be done in
5 cuts.
because
Simply imagine repeatedly folding it in half like a piece of paper until it is $1times1$. Instead of folding, you cut and stack the pieces on top of each other. If you are not allowed to stack on top of each other for the cut, then you can put them next to each other instead.
$4times 8 = 2^2 times 2^3$ so it takes 5 cuts to reduce to $2^0 times 2^0$.
answered 25 mins ago
Jaap Scherphuis
12.5k12155
add a comment |Â
up vote
3
down vote
up vote
3
down vote
It can be done in
5 cuts.
because
Simply imagine repeatedly folding it in half like a piece of paper until it is $1times1$. Instead of folding, you cut and stack the pieces on top of each other. If you are not allowed to stack on top of each other for the cut, then you can put them next to each other instead.
$4times 8 = 2^2 times 2^3$ so it takes 5 cuts to reduce to $2^0 times 2^0$.
answered 25 mins ago
Jaap Scherphuis
12.5k12155
It can be done in
5 cuts.
because
Simply imagine repeatedly folding it in half like a piece of paper until it is $1times1$. Instead of folding, you cut and stack the pieces on top of each other. If you are not allowed to stack on top of each other for the cut, then you can put them next to each other instead.
$4times 8 = 2^2 times 2^3$ so it takes 5 cuts to reduce to $2^0 times 2^0$.
answered 25 mins ago
Jaap Scherphuis
12.5k12155
edited 18 mins ago
answered 25 mins ago
Jaap Scherphuis
12.5k12155
answered 25 mins ago
Jaap Scherphuis
12.5k12155
answered 25 mins ago
Jaap Scherphuis
12.5k12155
12.5k12155
add a comment |Â
add a comment |Â
up vote
2
down vote
It may be done in
5 cuts if you are allowed to stack the pieces on top of each other after each cut.
Counting on this
First cut → two 4x4 pieces
Second cut → four 2x4 pieces
Third cut → eight 2x2 pieces
Fourth cut → sixteen 1x2 pieces
Fifth cut → thirty-two 1x1 squares
answered 25 mins ago
Tom
25.3k287148
add a comment |Â
up vote
2
down vote
It may be done in
5 cuts if you are allowed to stack the pieces on top of each other after each cut.
Counting on this
First cut → two 4x4 pieces
Second cut → four 2x4 pieces
Third cut → eight 2x2 pieces
Fourth cut → sixteen 1x2 pieces
Fifth cut → thirty-two 1x1 squares
answered 25 mins ago
Tom
25.3k287148
add a comment |Â
up vote
2
down vote
up vote
2
down vote
It may be done in
5 cuts if you are allowed to stack the pieces on top of each other after each cut.
Counting on this
First cut → two 4x4 pieces
Second cut → four 2x4 pieces
Third cut → eight 2x2 pieces
Fourth cut → sixteen 1x2 pieces
Fifth cut → thirty-two 1x1 squares
answered 25 mins ago
Tom
25.3k287148
It may be done in
5 cuts if you are allowed to stack the pieces on top of each other after each cut.
Counting on this
First cut → two 4x4 pieces
Second cut → four 2x4 pieces
Third cut → eight 2x2 pieces
Fourth cut → sixteen 1x2 pieces
Fifth cut → thirty-two 1x1 squares
answered 25 mins ago
Tom
25.3k287148
answered 25 mins ago
Tom
25.3k287148
answered 25 mins ago
Tom
25.3k287148
answered 25 mins ago
Tom
25.3k287148
25.3k287148
add a comment |Â
add a comment |Â
up vote
1
down vote
Total Cuts:
5
Method:
Cut in half vertically, creating 2, 2x8 pieces, then place these end to end to get a 2x16 piece. Cut again vertically through both pieces, to get 4, 1x8 pieces. Place these side by side to form a 4x8 piece again, this time, cut in half horizontally, and move the pieces to form an 8x4 shape, cut and move into 16x2, then cut once more and you have 32 individual pieces. This totals 5 cuts.
Explanation:
This puzzle works because with each cut, we half the size of every piece. to work this out quickly, we could do log2(32) = 5.
answered 19 mins ago
AHKieran
1,106216
add a comment |Â
up vote
1
down vote
Total Cuts:
5
Method:
Cut in half vertically, creating 2, 2x8 pieces, then place these end to end to get a 2x16 piece. Cut again vertically through both pieces, to get 4, 1x8 pieces. Place these side by side to form a 4x8 piece again, this time, cut in half horizontally, and move the pieces to form an 8x4 shape, cut and move into 16x2, then cut once more and you have 32 individual pieces. This totals 5 cuts.
Explanation:
This puzzle works because with each cut, we half the size of every piece. to work this out quickly, we could do log2(32) = 5.
answered 19 mins ago
AHKieran
1,106216
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Total Cuts:
5
Method:
Cut in half vertically, creating 2, 2x8 pieces, then place these end to end to get a 2x16 piece. Cut again vertically through both pieces, to get 4, 1x8 pieces. Place these side by side to form a 4x8 piece again, this time, cut in half horizontally, and move the pieces to form an 8x4 shape, cut and move into 16x2, then cut once more and you have 32 individual pieces. This totals 5 cuts.
Explanation:
This puzzle works because with each cut, we half the size of every piece. to work this out quickly, we could do log2(32) = 5.
answered 19 mins ago
AHKieran
1,106216
Total Cuts:
5
Method:
Cut in half vertically, creating 2, 2x8 pieces, then place these end to end to get a 2x16 piece. Cut again vertically through both pieces, to get 4, 1x8 pieces. Place these side by side to form a 4x8 piece again, this time, cut in half horizontally, and move the pieces to form an 8x4 shape, cut and move into 16x2, then cut once more and you have 32 individual pieces. This totals 5 cuts.
Explanation:
This puzzle works because with each cut, we half the size of every piece. to work this out quickly, we could do log2(32) = 5.
answered 19 mins ago
AHKieran
1,106216
answered 19 mins ago
AHKieran
1,106216
answered 19 mins ago
AHKieran
1,106216
answered 19 mins ago
AHKieran
1,106216
1,106216
add a comment |Â
add a comment |Â
up vote
1
down vote
The answer is
31 times
Because
you can either cut rows of 8 (3 cuts, you now have 4 rows of 8), then separate each row with 7 cuts each. $3 + (4*7) = 31$.
or cut vertically first seven times to create 8 columns of 4, then cut each 3 times. $7 + (8*3) = 31$.
changing between cutting horizontally and vertically each time will not help getting a lower amount of cuts. it always results in 31.
Unless..
we are allowed to cut 4 rows, put them together as if the bar were still whole, and cut 7 times vertically. In that case we get 11 cuts. I don't think this is allowed in this puzzle
After Q-Edit:
In this puzzle, we don't have to separate the pieces and cut each piece on its own. As others now have said, it is possible with 5 cuts.
What if putting chocolates onto each other was not allowed?- You don't even have to stack the halves on top of each other, just arrange them next to each other so you can cut each piece the same way with one cut.
answered 36 mins ago
Cashbee
1,19015
1
There are other possibilities. e.g. cut into two 2x8, then those into 2x2s, etc.
– Jaap Scherphuis
35 mins ago
@JaapScherphuis see edit
– Cashbee
35 mins ago
@Cashbee there is no restriction in the question.
– Oray
32 mins ago
1
@Oray well yes there is. from the inspiration-puzzle:and every time we cut the chocolate we separate the pieces and cut each piece on its own. you did not say that this is not valid anymore for your puzzle. Anyway, I covered both possibilities
– Cashbee
30 mins ago
1
To be fair, you had that exact sentence in your own question when I read it. I see it is now removed. Well played
– Cashbee
24 mins ago
 |Â
show 1 more comment
up vote
1
down vote
The answer is
31 times
Because
you can either cut rows of 8 (3 cuts, you now have 4 rows of 8), then separate each row with 7 cuts each. $3 + (4*7) = 31$.
or cut vertically first seven times to create 8 columns of 4, then cut each 3 times. $7 + (8*3) = 31$.
changing between cutting horizontally and vertically each time will not help getting a lower amount of cuts. it always results in 31.
Unless..
we are allowed to cut 4 rows, put them together as if the bar were still whole, and cut 7 times vertically. In that case we get 11 cuts. I don't think this is allowed in this puzzle
After Q-Edit:
In this puzzle, we don't have to separate the pieces and cut each piece on its own. As others now have said, it is possible with 5 cuts.
What if putting chocolates onto each other was not allowed?- You don't even have to stack the halves on top of each other, just arrange them next to each other so you can cut each piece the same way with one cut.
answered 36 mins ago
Cashbee
1,19015
1
There are other possibilities. e.g. cut into two 2x8, then those into 2x2s, etc.
– Jaap Scherphuis
35 mins ago
@JaapScherphuis see edit
– Cashbee
35 mins ago
@Cashbee there is no restriction in the question.
– Oray
32 mins ago
1
@Oray well yes there is. from the inspiration-puzzle:and every time we cut the chocolate we separate the pieces and cut each piece on its own. you did not say that this is not valid anymore for your puzzle. Anyway, I covered both possibilities
– Cashbee
30 mins ago
1
To be fair, you had that exact sentence in your own question when I read it. I see it is now removed. Well played
– Cashbee
24 mins ago
 |Â
show 1 more comment
up vote
1
down vote
up vote
1
down vote
The answer is
31 times
Because
you can either cut rows of 8 (3 cuts, you now have 4 rows of 8), then separate each row with 7 cuts each. $3 + (4*7) = 31$.
or cut vertically first seven times to create 8 columns of 4, then cut each 3 times. $7 + (8*3) = 31$.
changing between cutting horizontally and vertically each time will not help getting a lower amount of cuts. it always results in 31.
Unless..
we are allowed to cut 4 rows, put them together as if the bar were still whole, and cut 7 times vertically. In that case we get 11 cuts. I don't think this is allowed in this puzzle
After Q-Edit:
In this puzzle, we don't have to separate the pieces and cut each piece on its own. As others now have said, it is possible with 5 cuts.
What if putting chocolates onto each other was not allowed?- You don't even have to stack the halves on top of each other, just arrange them next to each other so you can cut each piece the same way with one cut.
answered 36 mins ago
Cashbee
1,19015
The answer is
31 times
Because
you can either cut rows of 8 (3 cuts, you now have 4 rows of 8), then separate each row with 7 cuts each. $3 + (4*7) = 31$.
or cut vertically first seven times to create 8 columns of 4, then cut each 3 times. $7 + (8*3) = 31$.
changing between cutting horizontally and vertically each time will not help getting a lower amount of cuts. it always results in 31.
Unless..
we are allowed to cut 4 rows, put them together as if the bar were still whole, and cut 7 times vertically. In that case we get 11 cuts. I don't think this is allowed in this puzzle
After Q-Edit:
In this puzzle, we don't have to separate the pieces and cut each piece on its own. As others now have said, it is possible with 5 cuts.
What if putting chocolates onto each other was not allowed?- You don't even have to stack the halves on top of each other, just arrange them next to each other so you can cut each piece the same way with one cut.
answered 36 mins ago
Cashbee
1,19015
edited 15 mins ago
answered 36 mins ago
Cashbee
1,19015
answered 36 mins ago
Cashbee
1,19015
answered 36 mins ago
Cashbee
1,19015
1,19015
1
There are other possibilities. e.g. cut into two 2x8, then those into 2x2s, etc.
– Jaap Scherphuis
35 mins ago
@JaapScherphuis see edit
– Cashbee
35 mins ago
@Cashbee there is no restriction in the question.
– Oray
32 mins ago
1
@Oray well yes there is. from the inspiration-puzzle:and every time we cut the chocolate we separate the pieces and cut each piece on its own. you did not say that this is not valid anymore for your puzzle. Anyway, I covered both possibilities
– Cashbee
30 mins ago
1
To be fair, you had that exact sentence in your own question when I read it. I see it is now removed. Well played
– Cashbee
24 mins ago
 |Â
show 1 more comment
1
There are other possibilities. e.g. cut into two 2x8, then those into 2x2s, etc.
– Jaap Scherphuis
35 mins ago
@JaapScherphuis see edit
– Cashbee
35 mins ago
@Cashbee there is no restriction in the question.
– Oray
32 mins ago
1
@Oray well yes there is. from the inspiration-puzzle:and every time we cut the chocolate we separate the pieces and cut each piece on its own. you did not say that this is not valid anymore for your puzzle. Anyway, I covered both possibilities
– Cashbee
30 mins ago
1
To be fair, you had that exact sentence in your own question when I read it. I see it is now removed. Well played
– Cashbee
24 mins ago
1
1
There are other possibilities. e.g. cut into two 2x8, then those into 2x2s, etc.
– Jaap Scherphuis
35 mins ago
There are other possibilities. e.g. cut into two 2x8, then those into 2x2s, etc.
– Jaap Scherphuis
35 mins ago
@JaapScherphuis see edit
– Cashbee
35 mins ago
@JaapScherphuis see edit
– Cashbee
35 mins ago
@Cashbee there is no restriction in the question.
– Oray
32 mins ago
@Cashbee there is no restriction in the question.
– Oray
32 mins ago
1
1
@Oray well yes there is. from the inspiration-puzzle:
and every time we cut the chocolate we separate the pieces and cut each piece on its own. you did not say that this is not valid anymore for your puzzle. Anyway, I covered both possibilities– Cashbee
30 mins ago
@Oray well yes there is. from the inspiration-puzzle:
and every time we cut the chocolate we separate the pieces and cut each piece on its own. you did not say that this is not valid anymore for your puzzle. Anyway, I covered both possibilities– Cashbee
30 mins ago
1
1
To be fair, you had that exact sentence in your own question when I read it. I see it is now removed. Well played
– Cashbee
24 mins ago
To be fair, you had that exact sentence in your own question when I read it. I see it is now removed. Well played
– Cashbee
24 mins ago
 |Â
show 1 more comment
up vote
0
down vote
0
because
Chocolate is usually already divided into
1 x 1blocks. You can easily crush it with your hand and you doesn't need any help of a knife.
I think that it is already divided into 32 blocks. Why would you provide dimensions4 x 8otherwise? Not2 x 4nor1 x 2?
answered 17 mins ago
mpasko256
99528
add a comment |Â
up vote
0
down vote
0
because
Chocolate is usually already divided into
1 x 1blocks. You can easily crush it with your hand and you doesn't need any help of a knife.
I think that it is already divided into 32 blocks. Why would you provide dimensions4 x 8otherwise? Not2 x 4nor1 x 2?
answered 17 mins ago
mpasko256
99528
add a comment |Â
up vote
0
down vote
up vote
0
down vote
0
because
Chocolate is usually already divided into
1 x 1blocks. You can easily crush it with your hand and you doesn't need any help of a knife.
I think that it is already divided into 32 blocks. Why would you provide dimensions4 x 8otherwise? Not2 x 4nor1 x 2?
answered 17 mins ago
mpasko256
99528
0
because
Chocolate is usually already divided into
1 x 1blocks. You can easily crush it with your hand and you doesn't need any help of a knife.
I think that it is already divided into 32 blocks. Why would you provide dimensions4 x 8otherwise? Not2 x 4nor1 x 2?
answered 17 mins ago
mpasko256
99528
edited 12 mins ago
answered 17 mins ago
mpasko256
99528
answered 17 mins ago
mpasko256
99528
answered 17 mins ago
mpasko256
99528
99528
add a comment |Â
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f73009%2fhard-4x8-chocolate-bar-riddle-v2%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Just to clarify, when you say least amount of cutting, does that mean the total length of all cuts?
– hexomino
40 mins ago
@hexomino total amount of cutting... not total length of cutting :)
– Oray
39 mins ago
My answer doesn't involve putting them on top of each other, but rearranging the cut pieces next to each other to achieve the same effect of cutting through multiple separate pieces in a single cutting action. Does this count?
– AHKieran
17 mins ago