Mixing
1984 - take the digits 1,9, 8 and 4 and Hard Challenges!
Clash Royale CLAN TAG#URR8PPP
up vote
1
down vote
favorite
This is kinda follow up question to:
Part II... Next year is the 70th anniversary of the publication of the
book 1984 by George Orwell. Here is a puzzle to start the anniversary
celebrations off a bit early ...
Can you assemble a formula using the numbers $1$, $9$, $8$, and $4$ in
any order so that the results equals.... You may use the operations
$x + y$, $x - y$, $x times y$, $x div y$, $x!$, $sqrtx$,
$sqrt[leftroot-2uproot2x]y$ and $x^y$, as long as all
operands are either $1$, $9$, $8$, or $4$. Operands may of course also
be derived from calculations e.g. $19*8*(sqrt4)$. You may also use
brackets to clarify order of operations, and you may concatenate two
or more of the four digits you start with (such as $8$ and $4$ to make
the number $84$) if you wish. You may only use each of the starting
digits once and you must use all four of them. I'm afraid that
concatenation of numbers from calculations is not permitted, but
answers with concatenations will get plus one from me.
Note that in all the puzzles above Double, triple, etc. factorials
(n-druple-factorials), such as $4!! = 4 times 2$ are not allowed, but
factorials of factorials are fine, such as $(4!)! = 24!$. I will
upvote answers with double, triple and n-druple-factorials which get
the required answers, but will not mark them as correct - particularly
because a general method was developed by @Carl Schildkraut to
solve these puzzles.
many thanks to the authors of the similar questions below for
inspiring this question.
This is part II after the first in this series was solved
- Use 2 0 1 and 8 to make 67
- Make numbers 93 using the digits 2, 0, 1, 8
- Make numbers 1 - 30 using the digits 2, 0, 1, 8
The same rules but there are some different challenges here.
Challenge No 1: Find 142 with the least amount of operations and parenthesis.
Challenge No 2: Find 87 with the least amount of operations and parenthesis.
Challenge No 3: Find 61
Challenge No 4: Find 71 without using power operation (only ^).
Challenge No 5: Find 46
Note that infinite square root is not allowed and I will accept the answer which includes all solutions.
mathematics
asked 1 hour ago
Oray
14.4k435141
add a comment |Â
up vote
1
down vote
favorite
This is kinda follow up question to:
Part II... Next year is the 70th anniversary of the publication of the
book 1984 by George Orwell. Here is a puzzle to start the anniversary
celebrations off a bit early ...
Can you assemble a formula using the numbers $1$, $9$, $8$, and $4$ in
any order so that the results equals.... You may use the operations
$x + y$, $x - y$, $x times y$, $x div y$, $x!$, $sqrtx$,
$sqrt[leftroot-2uproot2x]y$ and $x^y$, as long as all
operands are either $1$, $9$, $8$, or $4$. Operands may of course also
be derived from calculations e.g. $19*8*(sqrt4)$. You may also use
brackets to clarify order of operations, and you may concatenate two
or more of the four digits you start with (such as $8$ and $4$ to make
the number $84$) if you wish. You may only use each of the starting
digits once and you must use all four of them. I'm afraid that
concatenation of numbers from calculations is not permitted, but
answers with concatenations will get plus one from me.
Note that in all the puzzles above Double, triple, etc. factorials
(n-druple-factorials), such as $4!! = 4 times 2$ are not allowed, but
factorials of factorials are fine, such as $(4!)! = 24!$. I will
upvote answers with double, triple and n-druple-factorials which get
the required answers, but will not mark them as correct - particularly
because a general method was developed by @Carl Schildkraut to
solve these puzzles.
many thanks to the authors of the similar questions below for
inspiring this question.
This is part II after the first in this series was solved
- Use 2 0 1 and 8 to make 67
- Make numbers 93 using the digits 2, 0, 1, 8
- Make numbers 1 - 30 using the digits 2, 0, 1, 8
The same rules but there are some different challenges here.
Challenge No 1: Find 142 with the least amount of operations and parenthesis.
Challenge No 2: Find 87 with the least amount of operations and parenthesis.
Challenge No 3: Find 61
Challenge No 4: Find 71 without using power operation (only ^).
Challenge No 5: Find 46
Note that infinite square root is not allowed and I will accept the answer which includes all solutions.
mathematics
asked 1 hour ago
Oray
14.4k435141
Just double checking square root is counting as a power operation right?
– gabbo1092
46 mins ago
1
@gabbo1092 no, I count it as a different operation. adding that info in the question.
– Oray
45 mins ago
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
This is kinda follow up question to:
Part II... Next year is the 70th anniversary of the publication of the
book 1984 by George Orwell. Here is a puzzle to start the anniversary
celebrations off a bit early ...
Can you assemble a formula using the numbers $1$, $9$, $8$, and $4$ in
any order so that the results equals.... You may use the operations
$x + y$, $x - y$, $x times y$, $x div y$, $x!$, $sqrtx$,
$sqrt[leftroot-2uproot2x]y$ and $x^y$, as long as all
operands are either $1$, $9$, $8$, or $4$. Operands may of course also
be derived from calculations e.g. $19*8*(sqrt4)$. You may also use
brackets to clarify order of operations, and you may concatenate two
or more of the four digits you start with (such as $8$ and $4$ to make
the number $84$) if you wish. You may only use each of the starting
digits once and you must use all four of them. I'm afraid that
concatenation of numbers from calculations is not permitted, but
answers with concatenations will get plus one from me.
Note that in all the puzzles above Double, triple, etc. factorials
(n-druple-factorials), such as $4!! = 4 times 2$ are not allowed, but
factorials of factorials are fine, such as $(4!)! = 24!$. I will
upvote answers with double, triple and n-druple-factorials which get
the required answers, but will not mark them as correct - particularly
because a general method was developed by @Carl Schildkraut to
solve these puzzles.
many thanks to the authors of the similar questions below for
inspiring this question.
This is part II after the first in this series was solved
- Use 2 0 1 and 8 to make 67
- Make numbers 93 using the digits 2, 0, 1, 8
- Make numbers 1 - 30 using the digits 2, 0, 1, 8
The same rules but there are some different challenges here.
Challenge No 1: Find 142 with the least amount of operations and parenthesis.
Challenge No 2: Find 87 with the least amount of operations and parenthesis.
Challenge No 3: Find 61
Challenge No 4: Find 71 without using power operation (only ^).
Challenge No 5: Find 46
Note that infinite square root is not allowed and I will accept the answer which includes all solutions.
mathematics
asked 1 hour ago
Oray
14.4k435141
This is kinda follow up question to:
Part II... Next year is the 70th anniversary of the publication of the
book 1984 by George Orwell. Here is a puzzle to start the anniversary
celebrations off a bit early ...
Can you assemble a formula using the numbers $1$, $9$, $8$, and $4$ in
any order so that the results equals.... You may use the operations
$x + y$, $x - y$, $x times y$, $x div y$, $x!$, $sqrtx$,
$sqrt[leftroot-2uproot2x]y$ and $x^y$, as long as all
operands are either $1$, $9$, $8$, or $4$. Operands may of course also
be derived from calculations e.g. $19*8*(sqrt4)$. You may also use
brackets to clarify order of operations, and you may concatenate two
or more of the four digits you start with (such as $8$ and $4$ to make
the number $84$) if you wish. You may only use each of the starting
digits once and you must use all four of them. I'm afraid that
concatenation of numbers from calculations is not permitted, but
answers with concatenations will get plus one from me.
Note that in all the puzzles above Double, triple, etc. factorials
(n-druple-factorials), such as $4!! = 4 times 2$ are not allowed, but
factorials of factorials are fine, such as $(4!)! = 24!$. I will
upvote answers with double, triple and n-druple-factorials which get
the required answers, but will not mark them as correct - particularly
because a general method was developed by @Carl Schildkraut to
solve these puzzles.
many thanks to the authors of the similar questions below for
inspiring this question.
This is part II after the first in this series was solved
- Use 2 0 1 and 8 to make 67
- Make numbers 93 using the digits 2, 0, 1, 8
- Make numbers 1 - 30 using the digits 2, 0, 1, 8
The same rules but there are some different challenges here.
Challenge No 1: Find 142 with the least amount of operations and parenthesis.
Challenge No 2: Find 87 with the least amount of operations and parenthesis.
Challenge No 3: Find 61
Challenge No 4: Find 71 without using power operation (only ^).
Challenge No 5: Find 46
Note that infinite square root is not allowed and I will accept the answer which includes all solutions.
mathematics
mathematics
asked 1 hour ago
Oray
14.4k435141
asked 1 hour ago
Oray
14.4k435141
edited 45 mins ago
asked 1 hour ago
Oray
14.4k435141
asked 1 hour ago
Oray
14.4k435141
asked 1 hour ago
Oray
14.4k435141
14.4k435141
Just double checking square root is counting as a power operation right?
– gabbo1092
46 mins ago
1
@gabbo1092 no, I count it as a different operation. adding that info in the question.
– Oray
45 mins ago
add a comment |Â
Just double checking square root is counting as a power operation right?
– gabbo1092
46 mins ago
1
@gabbo1092 no, I count it as a different operation. adding that info in the question.
– Oray
45 mins ago
Just double checking square root is counting as a power operation right?
– gabbo1092
46 mins ago
Just double checking square root is counting as a power operation right?
– gabbo1092
46 mins ago
1
1
@gabbo1092 no, I count it as a different operation. adding that info in the question.
– Oray
45 mins ago
@gabbo1092 no, I count it as a different operation. adding that info in the question.
– Oray
45 mins ago
add a comment |Â
4 Answers
4
active
oldest
votes
up vote
3
down vote
accepted
Challenge No 1: Find 142 with the least amount of operations and parenthesis.
$148 - sqrt9! =142$
Challenge No 2: Find 87 with the least amount of operations and parenthesis.
$91 - 8 + 4 = 87$
Challenge No 3: Find 61
$1 + sqrt9!times (8 + sqrt4) =61$
Challenge No 4: Find 71 without using power operation (only ^).
$81 - sqrt9! -4 = 71$
Challenge No 5: Find 46
$sqrt9! times 8 - sqrt4 times 1 = 46$
edited 22 mins ago
Oray
14.4k435141
answered 38 mins ago
gabbo1092
71311
New contributor
gabbo1092 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
fyi: 142 and 87 are not found with the least amount of operations/parenthesis.
– Oray
36 mins ago
1
only Challenge No:2 is not okay, but the rest is done.
– Oray
27 mins ago
Will focus my efforts there
– gabbo1092
26 mins ago
add a comment |Â
up vote
1
down vote
Challenge no. 5 (46):
$$(8-1)^sqrt4-sqrt9=7^2-3=49-3=46$$
answered 38 mins ago
JonMark Perry
14.7k52972
add a comment |Â
up vote
1
down vote
Minimum amount of steps for 87 (Challenge No 2) :
$$sqrt841times9$$
answered 24 mins ago
Keelhaul
7,1332473
yes you got it :)
– Oray
22 mins ago
add a comment |Â
up vote
0
down vote
For 142:
$$sqrt4(9times8-1)=142$$
In order:
$$(-1+9times8)sqrt4=142$$
For 87:
$$8(9+sqrt4)-1$$
answered 45 mins ago
Joseph Mulligan
49410
fyi: 142 and 87 are not found with the least amount of operations/parenthesis.
– Oray
36 mins ago
add a comment |Â
4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
Challenge No 1: Find 142 with the least amount of operations and parenthesis.
$148 - sqrt9! =142$
Challenge No 2: Find 87 with the least amount of operations and parenthesis.
$91 - 8 + 4 = 87$
Challenge No 3: Find 61
$1 + sqrt9!times (8 + sqrt4) =61$
Challenge No 4: Find 71 without using power operation (only ^).
$81 - sqrt9! -4 = 71$
Challenge No 5: Find 46
$sqrt9! times 8 - sqrt4 times 1 = 46$
edited 22 mins ago
Oray
14.4k435141
answered 38 mins ago
gabbo1092
71311
New contributor
gabbo1092 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
fyi: 142 and 87 are not found with the least amount of operations/parenthesis.
– Oray
36 mins ago
1
only Challenge No:2 is not okay, but the rest is done.
– Oray
27 mins ago
Will focus my efforts there
– gabbo1092
26 mins ago
add a comment |Â
up vote
3
down vote
accepted
Challenge No 1: Find 142 with the least amount of operations and parenthesis.
$148 - sqrt9! =142$
Challenge No 2: Find 87 with the least amount of operations and parenthesis.
$91 - 8 + 4 = 87$
Challenge No 3: Find 61
$1 + sqrt9!times (8 + sqrt4) =61$
Challenge No 4: Find 71 without using power operation (only ^).
$81 - sqrt9! -4 = 71$
Challenge No 5: Find 46
$sqrt9! times 8 - sqrt4 times 1 = 46$
edited 22 mins ago
Oray
14.4k435141
answered 38 mins ago
gabbo1092
71311
New contributor
gabbo1092 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
fyi: 142 and 87 are not found with the least amount of operations/parenthesis.
– Oray
36 mins ago
1
only Challenge No:2 is not okay, but the rest is done.
– Oray
27 mins ago
Will focus my efforts there
– gabbo1092
26 mins ago
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
Challenge No 1: Find 142 with the least amount of operations and parenthesis.
$148 - sqrt9! =142$
Challenge No 2: Find 87 with the least amount of operations and parenthesis.
$91 - 8 + 4 = 87$
Challenge No 3: Find 61
$1 + sqrt9!times (8 + sqrt4) =61$
Challenge No 4: Find 71 without using power operation (only ^).
$81 - sqrt9! -4 = 71$
Challenge No 5: Find 46
$sqrt9! times 8 - sqrt4 times 1 = 46$
edited 22 mins ago
Oray
14.4k435141
answered 38 mins ago
gabbo1092
71311
New contributor
gabbo1092 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Challenge No 1: Find 142 with the least amount of operations and parenthesis.
$148 - sqrt9! =142$
Challenge No 2: Find 87 with the least amount of operations and parenthesis.
$91 - 8 + 4 = 87$
Challenge No 3: Find 61
$1 + sqrt9!times (8 + sqrt4) =61$
Challenge No 4: Find 71 without using power operation (only ^).
$81 - sqrt9! -4 = 71$
Challenge No 5: Find 46
$sqrt9! times 8 - sqrt4 times 1 = 46$
edited 22 mins ago
Oray
14.4k435141
answered 38 mins ago
gabbo1092
71311
New contributor
gabbo1092 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 22 mins ago
Oray
14.4k435141
edited 22 mins ago
Oray
14.4k435141
edited 22 mins ago
Oray
14.4k435141
14.4k435141
answered 38 mins ago
gabbo1092
71311
New contributor
gabbo1092 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 38 mins ago
gabbo1092
71311
answered 38 mins ago
gabbo1092
71311
71311
New contributor
gabbo1092 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
gabbo1092 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
gabbo1092 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
fyi: 142 and 87 are not found with the least amount of operations/parenthesis.
– Oray
36 mins ago
1
only Challenge No:2 is not okay, but the rest is done.
– Oray
27 mins ago
Will focus my efforts there
– gabbo1092
26 mins ago
add a comment |Â
fyi: 142 and 87 are not found with the least amount of operations/parenthesis.
– Oray
36 mins ago
1
only Challenge No:2 is not okay, but the rest is done.
– Oray
27 mins ago
Will focus my efforts there
– gabbo1092
26 mins ago
fyi: 142 and 87 are not found with the least amount of operations/parenthesis.
– Oray
36 mins ago
fyi: 142 and 87 are not found with the least amount of operations/parenthesis.
– Oray
36 mins ago
1
1
only Challenge No:2 is not okay, but the rest is done.
– Oray
27 mins ago
only Challenge No:2 is not okay, but the rest is done.
– Oray
27 mins ago
Will focus my efforts there
– gabbo1092
26 mins ago
Will focus my efforts there
– gabbo1092
26 mins ago
add a comment |Â
up vote
1
down vote
Challenge no. 5 (46):
$$(8-1)^sqrt4-sqrt9=7^2-3=49-3=46$$
answered 38 mins ago
JonMark Perry
14.7k52972
add a comment |Â
up vote
1
down vote
Challenge no. 5 (46):
$$(8-1)^sqrt4-sqrt9=7^2-3=49-3=46$$
answered 38 mins ago
JonMark Perry
14.7k52972
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Challenge no. 5 (46):
$$(8-1)^sqrt4-sqrt9=7^2-3=49-3=46$$
answered 38 mins ago
JonMark Perry
14.7k52972
Challenge no. 5 (46):
$$(8-1)^sqrt4-sqrt9=7^2-3=49-3=46$$
answered 38 mins ago
JonMark Perry
14.7k52972
answered 38 mins ago
JonMark Perry
14.7k52972
answered 38 mins ago
JonMark Perry
14.7k52972
answered 38 mins ago
JonMark Perry
14.7k52972
14.7k52972
add a comment |Â
add a comment |Â
up vote
1
down vote
Minimum amount of steps for 87 (Challenge No 2) :
$$sqrt841times9$$
answered 24 mins ago
Keelhaul
7,1332473
yes you got it :)
– Oray
22 mins ago
add a comment |Â
up vote
1
down vote
Minimum amount of steps for 87 (Challenge No 2) :
$$sqrt841times9$$
answered 24 mins ago
Keelhaul
7,1332473
yes you got it :)
– Oray
22 mins ago
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Minimum amount of steps for 87 (Challenge No 2) :
$$sqrt841times9$$
answered 24 mins ago
Keelhaul
7,1332473
Minimum amount of steps for 87 (Challenge No 2) :
$$sqrt841times9$$
answered 24 mins ago
Keelhaul
7,1332473
answered 24 mins ago
Keelhaul
7,1332473
answered 24 mins ago
Keelhaul
7,1332473
answered 24 mins ago
Keelhaul
7,1332473
7,1332473
yes you got it :)
– Oray
22 mins ago
add a comment |Â
yes you got it :)
– Oray
22 mins ago
yes you got it :)
– Oray
22 mins ago
yes you got it :)
– Oray
22 mins ago
add a comment |Â
up vote
0
down vote
For 142:
$$sqrt4(9times8-1)=142$$
In order:
$$(-1+9times8)sqrt4=142$$
For 87:
$$8(9+sqrt4)-1$$
answered 45 mins ago
Joseph Mulligan
49410
fyi: 142 and 87 are not found with the least amount of operations/parenthesis.
– Oray
36 mins ago
add a comment |Â
up vote
0
down vote
For 142:
$$sqrt4(9times8-1)=142$$
In order:
$$(-1+9times8)sqrt4=142$$
For 87:
$$8(9+sqrt4)-1$$
answered 45 mins ago
Joseph Mulligan
49410
fyi: 142 and 87 are not found with the least amount of operations/parenthesis.
– Oray
36 mins ago
add a comment |Â
up vote
0
down vote
up vote
0
down vote
For 142:
$$sqrt4(9times8-1)=142$$
In order:
$$(-1+9times8)sqrt4=142$$
For 87:
$$8(9+sqrt4)-1$$
answered 45 mins ago
Joseph Mulligan
49410
For 142:
$$sqrt4(9times8-1)=142$$
In order:
$$(-1+9times8)sqrt4=142$$
For 87:
$$8(9+sqrt4)-1$$
answered 45 mins ago
Joseph Mulligan
49410
edited 40 mins ago
answered 45 mins ago
Joseph Mulligan
49410
answered 45 mins ago
Joseph Mulligan
49410
answered 45 mins ago
Joseph Mulligan
49410
49410
fyi: 142 and 87 are not found with the least amount of operations/parenthesis.
– Oray
36 mins ago
add a comment |Â
fyi: 142 and 87 are not found with the least amount of operations/parenthesis.
– Oray
36 mins ago
fyi: 142 and 87 are not found with the least amount of operations/parenthesis.
– Oray
36 mins ago
fyi: 142 and 87 are not found with the least amount of operations/parenthesis.
– Oray
36 mins ago
add a comment |Â
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Just double checking square root is counting as a power operation right?
– gabbo1092
46 mins ago
1
@gabbo1092 no, I count it as a different operation. adding that info in the question.
– Oray
45 mins ago