please empty your brain below
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Just one expression each, thanks.
Simplest expression wins :)
Here are some operations you can cut and paste:
+-×÷()√!
Also "point four" is fine, that's ·4
and "point four recurring" can be ·4·
diamond geezer | Homepage | 04.04.22 - 4:03 p.m. | #
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1=(4+4)/(4+4)
Huw Thomas | 04.04.22 - 4:03 p.m. | #
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No, just two fours.
diamond geezer | Homepage | 04.04.22 - 4:04 p.m. | #
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(Embarrassed look)
1=4/4
Huw Thomas | 04.04.22 - 4:05 p.m. | #
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8 = 4+4
James | 04.04.22 - 4:05 p.m. | #
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6 = 4! / 4
Andrew | 04.04.22 - 4:06 p.m. | #
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6 = 4 + √4
Paul | 04.04.22 - 4:08 p.m. | #
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4=√(4×4)
RC | 04.04.22 - 4:08 p.m. | #
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4-4=0
Greg | 04.04.22 - 4:10 p.m. | #
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2 = 4 / √4.
Regards
zin92 | 04.04.22 - 4:13 p.m. | #
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7 =⌈√44⌉
dg writes: Not equal.
blart | 04.04.22 - 4:14 p.m. | #
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⌊4 - log(4)⌋ = 3
quin | 04.04.22 - 4:16 p.m. | #
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(those truncated square brackets are ceiling/floor functions that round up and down, so yes, I'd argue this is equal)
quin | 04.04.22 - 4:17 p.m. | #
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I'm not accepting ceiling/floor functions (except maybe as an absolute last resort).
diamond geezer | Homepage | 04.04.22 - 4:22 p.m. | #
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Log 4 (to base 4) = 10
[OK - I admit this isn't actually the number ten but it looks like it]
mushroomcounter | 04.04.22 - 4:50 p.m. | #
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I'm not accepting different number bases either :)
diamond geezer | Homepage | 04.04.22 - 4:52 p.m. | #
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You're accepting "to the power of 0.5" (ie square root), does this mean that we can use to the power of any number we like? Eg four squared, four cubed, four to the power of zero?
Thanks
zin92 | 04.04.22 - 5:08 p.m. | #
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Those use other digits (2, 3 & 0), so no.
diamond geezer | Homepage | 04.04.22 - 5:10 p.m. | #
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10 = 4/·4
M | 04.04.22 - 5:27 p.m. | #
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Just in case you end up accepting them as an absolute last resort:
9 = ⌊4! × ·4⌋
O | 04.04.22 - 5:43 p.m. | #
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The original Four Fours problem doesn't allow ⌊ ⌋ and ⌈ ⌉ because it's too easy that way... it's not proper arithmetic.
diamond geezer | Homepage | 04.04.22 - 5:53 p.m. | #
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how about 9 = 4 / ·4·
Q | 04.04.22 - 5:56 p.m. | #
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See, not necessary :)
diamond geezer | Homepage | 04.04.22 - 5:57 p.m. | #
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<snip>
Q | 04.04.22 - 5:59 p.m. | #
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does "just one expression each" mean one per question, or one per participant... because i have one more ;-)
Q | 04.04.22 - 6:05 p.m. | #
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That's your lot, thanks.
diamond geezer | Homepage | 04.04.22 - 6:05 p.m. | #
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Ah-ha!
5 = √4 / ·4
Harry Harrison | 04.04.22 - 6:46 p.m. | #
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Now that we've seen the solution for 9, 3 is easy:
3 = sqrt( 4 / ·4· )
Joachim | 04.04.22 - 7:57 p.m. | #
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3 = Γ4 / √4
Where Γ is the gamma function and
Γ(4) = (4− 1)! = 6
Geheee | 04.04.22 - 7:57 p.m. | #
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The simpler version wins :)
diamond geezer | Homepage | 04.04.22 - 7:59 p.m. | #
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Haha, yes that was over complicated…
How about:
7 = !4 - √4
Geheee | 04.04.22 - 8:03 p.m. | #
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I don't think the wider public are ready for subfactorials.
diamond geezer | Homepage | 04.04.22 - 8:11 p.m. | #
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So that's...
0 = 4 - 4
1 = 4 ÷ 4
2 = 4 ÷ √4
3 = √(4 ÷ ·4·)
4 = √4 + √4
5 = √4 ÷ ·4
6 = 4 + √4
...
8 = 4 + 4
9 = 4 ÷ ·4·
10 = 4 ÷ ·4
...and 7 remains complicated stuff
diamond geezer | Homepage | 04.04.22 - 10:00 p.m. | #
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7 = [(4^3 - 4^2 - 4^2) - 4] / 4
Sam | 05.04.22 - 1:00 a.m. | #
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Sorry, what do those dots in the expressions for 9 and 10 mean?
Patrickov | 05.04.22 - 2:03 a.m. | #
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No, two 4s.
That's five 4s, two 2s and a 3.
diamond geezer | Homepage | 05.04.22 - 7:30 a.m. | #
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·4 = 0.4
·4· = 0.44444444444...
diamond geezer | Homepage | 05.04.22 - 7:36 a.m. | #
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7 = ceiling ( sqrt 44 )
Cheating, of course, but close!
Chris | 05.04.22 - 9:09 a.m. | #
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Someone’s already tried that.
diamond geezer | Homepage | 05.04.22 - 9:21 a.m. | #
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7 = Perfect(√4 ) / 4
yerrong | 05.04.22 - 12:39 p.m. | #
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Strayed a very long way from "common mathematical symbols" there...
diamond geezer | Homepage | 05.04.22 - 3:57 p.m. | #
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7=4+4-(4/4)
Rob | 05.04.22 - 11:36 p.m. | #
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No, two fours.
diamond geezer | Homepage | 05.04.22 - 11:37 p.m. | #
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7 = (4! / 4)++
buz | 06.04.22 - 3:18 p.m. | #
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I would note, without offering an expression, that 7 happens to be the fourth prime number.
Chris | 07.04.22 - 8:53 a.m. | #
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