Are there any other shorter expressions for 8 by manipulating exactly 4 4?
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The label $4times 4 -4 -4$ for 8 seems to be too long. I am looking for other shorter ones while maintaining the constraint of only using four 4.
Are there such expressions?
integer-partitions
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add a comment |
$begingroup$
The label $4times 4 -4 -4$ for 8 seems to be too long. I am looking for other shorter ones while maintaining the constraint of only using four 4.
Are there such expressions?
integer-partitions
$endgroup$
2
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What about $(4+4)cdotfrac{4}{4}$? :-D
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– trancelocation
27 mins ago
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@trancelocation : nice thanks!
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– Artificial Stupidity
26 mins ago
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Another one $4cdotsqrt[4]{4cdot 4}$.
$endgroup$
– trancelocation
23 mins ago
add a comment |
$begingroup$
The label $4times 4 -4 -4$ for 8 seems to be too long. I am looking for other shorter ones while maintaining the constraint of only using four 4.
Are there such expressions?
integer-partitions
$endgroup$
The label $4times 4 -4 -4$ for 8 seems to be too long. I am looking for other shorter ones while maintaining the constraint of only using four 4.
Are there such expressions?
integer-partitions
integer-partitions
asked 31 mins ago
Artificial StupidityArtificial Stupidity
355110
355110
2
$begingroup$
What about $(4+4)cdotfrac{4}{4}$? :-D
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– trancelocation
27 mins ago
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@trancelocation : nice thanks!
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– Artificial Stupidity
26 mins ago
$begingroup$
Another one $4cdotsqrt[4]{4cdot 4}$.
$endgroup$
– trancelocation
23 mins ago
add a comment |
2
$begingroup$
What about $(4+4)cdotfrac{4}{4}$? :-D
$endgroup$
– trancelocation
27 mins ago
$begingroup$
@trancelocation : nice thanks!
$endgroup$
– Artificial Stupidity
26 mins ago
$begingroup$
Another one $4cdotsqrt[4]{4cdot 4}$.
$endgroup$
– trancelocation
23 mins ago
2
2
$begingroup$
What about $(4+4)cdotfrac{4}{4}$? :-D
$endgroup$
– trancelocation
27 mins ago
$begingroup$
What about $(4+4)cdotfrac{4}{4}$? :-D
$endgroup$
– trancelocation
27 mins ago
$begingroup$
@trancelocation : nice thanks!
$endgroup$
– Artificial Stupidity
26 mins ago
$begingroup$
@trancelocation : nice thanks!
$endgroup$
– Artificial Stupidity
26 mins ago
$begingroup$
Another one $4cdotsqrt[4]{4cdot 4}$.
$endgroup$
– trancelocation
23 mins ago
$begingroup$
Another one $4cdotsqrt[4]{4cdot 4}$.
$endgroup$
– trancelocation
23 mins ago
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Here is one: $frac{4times4}4+4=8$
Here is another one: $frac{4!}{4-frac44}=8$
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$begingroup$
I accept this answer because the second is relatively short.
$endgroup$
– Artificial Stupidity
4 mins ago
add a comment |
$begingroup$
Here my ones: :-)
- $(4+4)timesfrac{4}{4}$
- $4times sqrt[4]{4times 4}$
$endgroup$
$begingroup$
The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
$endgroup$
– Misha Lavrov
18 mins ago
$begingroup$
@MishaLavrov right. adjusted accordingly. :-)
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– trancelocation
8 mins ago
add a comment |
$begingroup$
We have $8=4+4^{4/4}$, which plays nicely with your existing $4=4+4^{4-4}$.
Edit: Or $8=4+log_4 4^4=log_4 4^{4+4}$, if you want to bring in a new ingredient.
$endgroup$
add a comment |
Your Answer
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Here is one: $frac{4times4}4+4=8$
Here is another one: $frac{4!}{4-frac44}=8$
$endgroup$
$begingroup$
I accept this answer because the second is relatively short.
$endgroup$
– Artificial Stupidity
4 mins ago
add a comment |
$begingroup$
Here is one: $frac{4times4}4+4=8$
Here is another one: $frac{4!}{4-frac44}=8$
$endgroup$
$begingroup$
I accept this answer because the second is relatively short.
$endgroup$
– Artificial Stupidity
4 mins ago
add a comment |
$begingroup$
Here is one: $frac{4times4}4+4=8$
Here is another one: $frac{4!}{4-frac44}=8$
$endgroup$
Here is one: $frac{4times4}4+4=8$
Here is another one: $frac{4!}{4-frac44}=8$
answered 26 mins ago
abc...abc...
2,337532
2,337532
$begingroup$
I accept this answer because the second is relatively short.
$endgroup$
– Artificial Stupidity
4 mins ago
add a comment |
$begingroup$
I accept this answer because the second is relatively short.
$endgroup$
– Artificial Stupidity
4 mins ago
$begingroup$
I accept this answer because the second is relatively short.
$endgroup$
– Artificial Stupidity
4 mins ago
$begingroup$
I accept this answer because the second is relatively short.
$endgroup$
– Artificial Stupidity
4 mins ago
add a comment |
$begingroup$
Here my ones: :-)
- $(4+4)timesfrac{4}{4}$
- $4times sqrt[4]{4times 4}$
$endgroup$
$begingroup$
The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
$endgroup$
– Misha Lavrov
18 mins ago
$begingroup$
@MishaLavrov right. adjusted accordingly. :-)
$endgroup$
– trancelocation
8 mins ago
add a comment |
$begingroup$
Here my ones: :-)
- $(4+4)timesfrac{4}{4}$
- $4times sqrt[4]{4times 4}$
$endgroup$
$begingroup$
The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
$endgroup$
– Misha Lavrov
18 mins ago
$begingroup$
@MishaLavrov right. adjusted accordingly. :-)
$endgroup$
– trancelocation
8 mins ago
add a comment |
$begingroup$
Here my ones: :-)
- $(4+4)timesfrac{4}{4}$
- $4times sqrt[4]{4times 4}$
$endgroup$
Here my ones: :-)
- $(4+4)timesfrac{4}{4}$
- $4times sqrt[4]{4times 4}$
edited 9 mins ago
answered 22 mins ago
trancelocationtrancelocation
10.5k1722
10.5k1722
$begingroup$
The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
$endgroup$
– Misha Lavrov
18 mins ago
$begingroup$
@MishaLavrov right. adjusted accordingly. :-)
$endgroup$
– trancelocation
8 mins ago
add a comment |
$begingroup$
The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
$endgroup$
– Misha Lavrov
18 mins ago
$begingroup$
@MishaLavrov right. adjusted accordingly. :-)
$endgroup$
– trancelocation
8 mins ago
$begingroup$
The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
$endgroup$
– Misha Lavrov
18 mins ago
$begingroup$
The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
$endgroup$
– Misha Lavrov
18 mins ago
$begingroup$
@MishaLavrov right. adjusted accordingly. :-)
$endgroup$
– trancelocation
8 mins ago
$begingroup$
@MishaLavrov right. adjusted accordingly. :-)
$endgroup$
– trancelocation
8 mins ago
add a comment |
$begingroup$
We have $8=4+4^{4/4}$, which plays nicely with your existing $4=4+4^{4-4}$.
Edit: Or $8=4+log_4 4^4=log_4 4^{4+4}$, if you want to bring in a new ingredient.
$endgroup$
add a comment |
$begingroup$
We have $8=4+4^{4/4}$, which plays nicely with your existing $4=4+4^{4-4}$.
Edit: Or $8=4+log_4 4^4=log_4 4^{4+4}$, if you want to bring in a new ingredient.
$endgroup$
add a comment |
$begingroup$
We have $8=4+4^{4/4}$, which plays nicely with your existing $4=4+4^{4-4}$.
Edit: Or $8=4+log_4 4^4=log_4 4^{4+4}$, if you want to bring in a new ingredient.
$endgroup$
We have $8=4+4^{4/4}$, which plays nicely with your existing $4=4+4^{4-4}$.
Edit: Or $8=4+log_4 4^4=log_4 4^{4+4}$, if you want to bring in a new ingredient.
answered 23 mins ago
Chris CulterChris Culter
20.3k43584
20.3k43584
add a comment |
add a comment |
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2
$begingroup$
What about $(4+4)cdotfrac{4}{4}$? :-D
$endgroup$
– trancelocation
27 mins ago
$begingroup$
@trancelocation : nice thanks!
$endgroup$
– Artificial Stupidity
26 mins ago
$begingroup$
Another one $4cdotsqrt[4]{4cdot 4}$.
$endgroup$
– trancelocation
23 mins ago