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## Fun Math/Logic Problems!

Started by _iPhoenix_, March 17, 2017, 09:54:08 PM

0 Members and 1 Guest are viewing this topic.

#### _iPhoenix_

I got one!

With 5 eight's, and 5 basic operators (+, -, *, /, ^, plus parenthesis, of course.), is it possible to get the numbers 1 - 16 (It may be no, 16 is arbitrary )?
If so: how, and how far can you go (continuously after 10)?

E.X.
(8/8)^8-(8/8) = 0

jonbush asked a very good question:
Quote from: jonbushSo we must use all five 8's, but we can use any number of operators?

Yes. NO OPERATORS/OPERATIONS NOT MENTIONED!

And no programs to try every single combo, either. Fine... I used one myself to solve it anyway...

And if you do create a program, you need to explain (prove, in short) why that particular one is impossible...

Hints (filthy cheater ):

Hint #1
Hint #2

• Calculators owned: Two TI-84+ CE's

"walruses are better than tuxedo chickens, all hail the great " ~ me
Evolution of my avatar:

#### c4ooo

#1
Quote from: _iPhoenix_ on March 17, 2017, 09:54:08 PM
And no programs to try every single combo, either.[/s]
What's a program?

Spoiler

(((8+8)+8)+8)+8 = 40.0
(((8+8)+8)+8)-8 = 24.0
(((8+8)+8)+8)*8 = 256.0
(((8+8)+8)+8)/8 = 4.0
(((8+8)+8)-8)+8 = 24.0
(((8+8)+8)-8)-8 = 8.0
(((8+8)+8)-8)*8 = 128.0
(((8+8)+8)-8)/8 = 2.0
(((8+8)+8)*+8 = 200.0
(((8+8)+8)*-8 = 184.0
(((8+8)+8)**8 = 1536.0
(((8+8)+8)*/8 = 24.0
(((8+8)+8)/8)+8 = 11.0
(((8+8)+8)/8)-8 = -5.0
(((8+8)+8)/8)*8 = 24.0
(((8+8)+8)/8)^8 = 6561.0
(((8+8)-8)+8)+8 = 24.0
(((8+8)-8)+8)-8 = 8.0
(((8+8)-8)+8)*8 = 128.0
(((8+8)-8)+8)/8 = 2.0
(((8+8)-8)-8)+8 = 8.0
(((8+8)-8)-8)-8 = -8.0
(((8+8)-8)-8)*8 = 0.0
(((8+8)-8)-8)/8 = 0.0
(((8+8)-8)-8)^8 = 0.0
(((8+8)-8)*+8 = 72.0
(((8+8)-8)*-8 = 56.0
(((8+8)-8)**8 = 512.0
(((8+8)-8)*/8 = 8.0
(((8+8)-8)/8)+8 = 9.0
(((8+8)-8)/8)-8 = -7.0
(((8+8)-8)/8)*8 = 8.0
(((8+8)-8)/8)^8 = 1.0
(((8+8)-8)^8)+8 = 1.6777224E7
(((8+8)-8)^8)-8 = 1.6777208E7
(((8+8)-8)^8)*8 = 1.34217728E8
(((8+8)-8)^8)/8 = 2097152.0
(((8+8)*+8)+8 = 144.0
(((8+8)*+8)-8 = 128.0
(((8+8)*+8)*8 = 1088.0
(((8+8)*+8)/8 = 17.0
(((8+8)*-8)+8 = 128.0
(((8+8)*-8)-8 = 112.0
(((8+8)*-8)*8 = 960.0
(((8+8)*-8)/8 = 15.0
(((8+8)**+8 = 1032.0
(((8+8)**-8 = 1016.0
(((8+8)***8 = 8192.0
(((8+8)**/8 = 128.0
(((8+8)*/8)+8 = 24.0
(((8+8)*/8)-8 = 8.0
(((8+8)*/8)*8 = 128.0
(((8+8)*/8)/8 = 2.0
(((8+8)/8)+8)+8 = 18.0
(((8+8)/8)+8)-8 = 2.0
(((8+8)/8)+8)*8 = 80.0
(((8+8)/8)+8)^8 = 1.0E8
(((8+8)/8)-8)+8 = 2.0
(((8+8)/8)-8)-8 = -14.0
(((8+8)/8)-8)*8 = -48.0
(((8+8)/8)-8)^8 = 1679616.0
(((8+8)/8)*+8 = 24.0
(((8+8)/8)*-8 = 8.0
(((8+8)/8)**8 = 128.0
(((8+8)/8)*/8 = 2.0
(((8+8)/8)/8)*8 = 2.0
(((8+8)/8)^8)+8 = 264.0
(((8+8)/8)^8)-8 = 248.0
(((8+8)/8)^8)*8 = 2048.0
(((8+8)/8)^8)/8 = 32.0
(((8+8)^8)+8)/8 = 5.3687091E8
(((8+8)^8)-8)/8 = 5.3687091E8
(((8+8)^8)/8)+8 = 5.3687091E8
(((8+8)^8)/8)-8 = 5.3687091E8
(((8+8)^8)/8)/8 = 6.7108864E7
(((8-8)+8)+8)+8 = 24.0
(((8-8)+8)+8)-8 = 8.0
(((8-8)+8)+8)*8 = 128.0
(((8-8)+8)+8)/8 = 2.0
(((8-8)+8)-8)+8 = 8.0
(((8-8)+8)-8)-8 = -8.0
(((8-8)+8)-8)*8 = 0.0
(((8-8)+8)-8)/8 = 0.0
(((8-8)+8)-8)^8 = 0.0
(((8-8)+8)*+8 = 72.0
(((8-8)+8)*-8 = 56.0
(((8-8)+8)**8 = 512.0
(((8-8)+8)*/8 = 8.0
(((8-8)+8)/8)+8 = 9.0
(((8-8)+8)/8)-8 = -7.0
(((8-8)+8)/8)*8 = 8.0
(((8-8)+8)/8)^8 = 1.0
(((8-8)+8)^8)+8 = 1.6777224E7
(((8-8)+8)^8)-8 = 1.6777208E7
(((8-8)+8)^8)*8 = 1.34217728E8
(((8-8)+8)^8)/8 = 2097152.0
(((8-8)-8)+8)+8 = 8.0
(((8-8)-8)+8)-8 = -8.0
(((8-8)-8)+8)*8 = 0.0
(((8-8)-8)+8)/8 = 0.0
(((8-8)-8)+8)^8 = 0.0
(((8-8)-8)-8)+8 = -8.0
(((8-8)-8)-8)-8 = -24.0
(((8-8)-8)-8)*8 = -128.0
(((8-8)-8)-8)/8 = -2.0
(((8-8)-8)*+8 = -56.0
(((8-8)-8)*-8 = -72.0
(((8-8)-8)**8 = -512.0
(((8-8)-8)*/8 = -8.0
(((8-8)-8)/8)+8 = 7.0
(((8-8)-8)/8)-8 = -9.0
(((8-8)-8)/8)*8 = -8.0
(((8-8)-8)/8)^8 = 1.0
(((8-8)-8)^8)+8 = 1.6777224E7
(((8-8)-8)^8)-8 = 1.6777208E7
(((8-8)-8)^8)*8 = 1.34217728E8
(((8-8)-8)^8)/8 = 2097152.0
(((8-8)*+8)+8 = 16.0
(((8-8)*+8)-8 = 0.0
(((8-8)*+8)*8 = 64.0
(((8-8)*+8)/8 = 1.0
(((8-8)*+8)^8 = 1.6777216E7
(((8-8)*-8)+8 = 0.0
(((8-8)*-8)-8 = -16.0
(((8-8)*-8)*8 = -64.0
(((8-8)*-8)/8 = -1.0
(((8-8)*-8)^8 = 1.6777216E7
(((8-8)**+8 = 8.0
(((8-8)**-8 = -8.0
(((8-8)***8 = 0.0
(((8-8)**/8 = 0.0
(((8-8)**^8 = 0.0
(((8-8)*/8)+8 = 8.0
(((8-8)*/8)-8 = -8.0
(((8-8)*/8)*8 = 0.0
(((8-8)*/8)/8 = 0.0
(((8-8)*/8)^8 = 0.0
(((8-8)*^8)+8 = 8.0
(((8-8)*^8)-8 = -8.0
(((8-8)*^8)*8 = 0.0
(((8-8)*^8)/8 = 0.0
(((8-8)*^8)^8 = 0.0
(((8-8)/8)+8)+8 = 16.0
(((8-8)/8)+8)-8 = 0.0
(((8-8)/8)+8)*8 = 64.0
(((8-8)/8)+8)/8 = 1.0
(((8-8)/8)+8)^8 = 1.6777216E7
(((8-8)/8)-8)+8 = 0.0
(((8-8)/8)-8)-8 = -16.0
(((8-8)/8)-8)*8 = -64.0
(((8-8)/8)-8)/8 = -1.0
(((8-8)/8)-8)^8 = 1.6777216E7
(((8-8)/8)*+8 = 8.0
(((8-8)/8)*-8 = -8.0
(((8-8)/8)**8 = 0.0
(((8-8)/8)*/8 = 0.0
(((8-8)/8)*^8 = 0.0
(((8-8)/8)/8)+8 = 8.0
(((8-8)/8)/8)-8 = -8.0
(((8-8)/8)/8)*8 = 0.0
(((8-8)/8)/8)/8 = 0.0
(((8-8)/8)/8)^8 = 0.0
(((8-8)/8)^8)+8 = 8.0
(((8-8)/8)^8)-8 = -8.0
(((8-8)/8)^8)*8 = 0.0
(((8-8)/8)^8)/8 = 0.0
(((8-8)/8)^8)^8 = 0.0
(((8-8)^8)+8)+8 = 16.0
(((8-8)^8)+8)-8 = 0.0
(((8-8)^8)+8)*8 = 64.0
(((8-8)^8)+8)/8 = 1.0
(((8-8)^8)+8)^8 = 1.6777216E7
(((8-8)^8)-8)+8 = 0.0
(((8-8)^8)-8)-8 = -16.0
(((8-8)^8)-8)*8 = -64.0
(((8-8)^8)-8)/8 = -1.0
(((8-8)^8)-8)^8 = 1.6777216E7
(((8-8)^8)*+8 = 8.0
(((8-8)^8)*-8 = -8.0
(((8-8)^8)**8 = 0.0
(((8-8)^8)*/8 = 0.0
(((8-8)^8)*^8 = 0.0
(((8-8)^8)/8)+8 = 8.0
(((8-8)^8)/8)-8 = -8.0
(((8-8)^8)/8)*8 = 0.0
(((8-8)^8)/8)/8 = 0.0
(((8-8)^8)/8)^8 = 0.0
(((8-8)^8)^8)+8 = 8.0
(((8-8)^8)^8)-8 = -8.0
(((8-8)^8)^8)*8 = 0.0
(((8-8)^8)^8)/8 = 0.0
(((8-8)^8)^8)^8 = 0.0
(((8*+8)+8)+8 = 88.0
(((8*+8)+8)-8 = 72.0
(((8*+8)+8)*8 = 640.0
(((8*+8)+8)/8 = 10.0
(((8*+8)-8)+8 = 72.0
(((8*+8)-8)-8 = 56.0
(((8*+8)-8)*8 = 512.0
(((8*+8)-8)/8 = 8.0
(((8*+8)*+8 = 584.0
(((8*+8)*-8 = 568.0
(((8*+8)**8 = 4608.0
(((8*+8)*/8 = 72.0
(((8*+8)/8)+8 = 17.0
(((8*+8)/8)-8 = 1.0
(((8*+8)/8)*8 = 72.0
(((8*+8)/8)^8 = 4.304672E7
(((8*-8)+8)+8 = 72.0
(((8*-8)+8)-8 = 56.0
(((8*-8)+8)*8 = 512.0
(((8*-8)+8)/8 = 8.0
(((8*-8)-8)+8 = 56.0
(((8*-8)-8)-8 = 40.0
(((8*-8)-8)*8 = 384.0
(((8*-8)-8)/8 = 6.0
(((8*-8)*+8 = 456.0
(((8*-8)*-8 = 440.0
(((8*-8)**8 = 3584.0
(((8*-8)*/8 = 56.0
(((8*-8)/8)+8 = 15.0
(((8*-8)/8)-8 = -1.0
(((8*-8)/8)*8 = 56.0
(((8*-8)/8)^8 = 5764801.0
(((8**+8)+8 = 528.0
(((8**+8)-8 = 512.0
(((8**+8)*8 = 4160.0
(((8**+8)/8 = 65.0
(((8**-8)+8 = 512.0
(((8**-8)-8 = 496.0
(((8**-8)*8 = 4032.0
(((8**-8)/8 = 63.0
(((8***+8 = 4104.0
(((8***-8 = 4088.0
(((8****8 = 32768.0
(((8***/8 = 512.0
(((8**/8)+8 = 72.0
(((8**/8)-8 = 56.0
(((8**/8)*8 = 512.0
(((8**/8)/8 = 8.0
(((8*/8)+8)+8 = 24.0
(((8*/8)+8)-8 = 8.0
(((8*/8)+8)*8 = 128.0
(((8*/8)+8)/8 = 2.0
(((8*/8)-8)+8 = 8.0
(((8*/8)-8)-8 = -8.0
(((8*/8)-8)*8 = 0.0
(((8*/8)-8)/8 = 0.0
(((8*/8)-8)^8 = 0.0
(((8*/8)*+8 = 72.0
(((8*/8)*-8 = 56.0
(((8*/8)**8 = 512.0
(((8*/8)*/8 = 8.0
(((8*/8)/8)+8 = 9.0
(((8*/8)/8)-8 = -7.0
(((8*/8)/8)*8 = 8.0
(((8*/8)/8)^8 = 1.0
(((8*/8)^8)+8 = 1.6777224E7
(((8*/8)^8)-8 = 1.6777208E7
(((8*/8)^8)*8 = 1.34217728E8
(((8*/8)^8)/8 = 2097152.0
(((8/8)+8)+8)+8 = 25.0
(((8/8)+8)+8)-8 = 9.0
(((8/8)+8)+8)*8 = 136.0
(((8/8)+8)-8)+8 = 9.0
(((8/8)+8)-8)-8 = -7.0
(((8/8)+8)-8)*8 = 8.0
(((8/8)+8)-8)^8 = 1.0
(((8/8)+8)*+8 = 80.0
(((8/8)+8)*-8 = 64.0
(((8/8)+8)**8 = 576.0
(((8/8)+8)*/8 = 9.0
(((8/8)+8)/8)*8 = 9.0
(((8/8)+8)^8)+8 = 4.3046728E7
(((8/8)+8)^8)-8 = 4.3046712E7
(((8/8)+8)^8)*8 = 3.4437376E8
(((8/8)+8)^8)/8 = 5380840.0
(((8/8)-8)+8)+8 = 9.0
(((8/8)-8)+8)-8 = -7.0
(((8/8)-8)+8)*8 = 8.0
(((8/8)-8)+8)^8 = 1.0
(((8/8)-8)-8)+8 = -7.0
(((8/8)-8)-8)-8 = -23.0
(((8/8)-8)-8)*8 = -120.0
(((8/8)-8)*+8 = -48.0
(((8/8)-8)*-8 = -64.0
(((8/8)-8)**8 = -448.0
(((8/8)-8)*/8 = -7.0
(((8/8)-8)/8)*8 = -7.0
(((8/8)-8)^8)+8 = 5764809.0
(((8/8)-8)^8)-8 = 5764793.0
(((8/8)-8)^8)*8 = 4.6118408E7
(((8/8)*+8)+8 = 24.0
(((8/8)*+8)-8 = 8.0
(((8/8)*+8)*8 = 128.0
(((8/8)*+8)/8 = 2.0
(((8/8)*-8)+8 = 8.0
(((8/8)*-8)-8 = -8.0
(((8/8)*-8)*8 = 0.0
(((8/8)*-8)/8 = 0.0
(((8/8)*-8)^8 = 0.0
(((8/8)**+8 = 72.0
(((8/8)**-8 = 56.0
(((8/8)***8 = 512.0
(((8/8)**/8 = 8.0
(((8/8)*/8)+8 = 9.0
(((8/8)*/8)-8 = -7.0
(((8/8)*/8)*8 = 8.0
(((8/8)*/8)^8 = 1.0
(((8/8)*^8)+8 = 1.6777224E7
(((8/8)*^8)-8 = 1.6777208E7
(((8/8)*^8)*8 = 1.34217728E8
(((8/8)*^8)/8 = 2097152.0
(((8/8)/8)+8)*8 = 65.0
(((8/8)/8)+8)^8 = 1.899271E7
(((8/8)/8)-8)*8 = -63.0
(((8/8)/8)-8)^8 = 1.4791237E7
(((8/8)/8)*+8 = 9.0
(((8/8)/8)*-8 = -7.0
(((8/8)/8)**8 = 8.0
(((8/8)/8)*^8 = 1.0
(((8/8)/8)^8)+8 = 8.0
(((8/8)/8)^8)-8 = -8.0
(((8/8)/8)^8)^8 = 0.0
(((8/8)^8)+8)+8 = 17.0
(((8/8)^8)+8)-8 = 1.0
(((8/8)^8)+8)*8 = 72.0
(((8/8)^8)+8)^8 = 4.304672E7
(((8/8)^8)-8)+8 = 1.0
(((8/8)^8)-8)-8 = -15.0
(((8/8)^8)-8)*8 = -56.0
(((8/8)^8)-8)^8 = 5764801.0
(((8/8)^8)*+8 = 16.0
(((8/8)^8)*-8 = 0.0
(((8/8)^8)**8 = 64.0
(((8/8)^8)*/8 = 1.0
(((8/8)^8)*^8 = 1.6777216E7
(((8/8)^8)/8)*8 = 1.0
(((8/8)^8)^8)+8 = 9.0
(((8/8)^8)^8)-8 = -7.0
(((8/8)^8)^8)*8 = 8.0
(((8/8)^8)^8)^8 = 1.0
(((8^8)+8)+8)+8 = 1.677724E7
(((8^8)+8)+8)-8 = 1.6777224E7
(((8^8)+8)+8)*8 = 1.34217856E8
(((8^8)+8)+8)/8 = 2097154.0
(((8^8)+8)-8)+8 = 1.6777224E7
(((8^8)+8)-8)-8 = 1.6777208E7
(((8^8)+8)-8)*8 = 1.34217728E8
(((8^8)+8)-8)/8 = 2097152.0
(((8^8)+8)*+8 = 1.34217792E8
(((8^8)+8)*-8 = 1.34217792E8
(((8^8)+8)**8 = 1.07374234E9
(((8^8)+8)*/8 = 1.6777224E7
(((8^8)+8)/8)+8 = 2097161.0
(((8^8)+8)/8)-8 = 2097145.0
(((8^8)+8)/8)*8 = 1.6777224E7
(((8^8)-8)+8)+8 = 1.6777224E7
(((8^8)-8)+8)-8 = 1.6777208E7
(((8^8)-8)+8)*8 = 1.34217728E8
(((8^8)-8)+8)/8 = 2097152.0
(((8^8)-8)-8)+8 = 1.6777208E7
(((8^8)-8)-8)-8 = 1.6777192E7
(((8^8)-8)-8)*8 = 1.342176E8
(((8^8)-8)-8)/8 = 2097150.0
(((8^8)-8)*+8 = 1.34217672E8
(((8^8)-8)*-8 = 1.34217656E8
(((8^8)-8)**8 = 1.07374131E9
(((8^8)-8)*/8 = 1.6777208E7
(((8^8)-8)/8)+8 = 2097159.0
(((8^8)-8)/8)-8 = 2097143.0
(((8^8)-8)/8)*8 = 1.6777208E7
(((8^8)*+8)+8 = 1.34217728E8
(((8^8)*+8)-8 = 1.3421772E8
(((8^8)*+8)*8 = 1.07374182E9
(((8^8)*+8)/8 = 1.6777216E7
(((8^8)*-8)+8 = 1.34217728E8
(((8^8)*-8)-8 = 1.34217712E8
(((8^8)*-8)*8 = 1.07374176E9
(((8^8)*-8)/8 = 1.6777215E7
(((8^8)**+8 = 1.07374182E9
(((8^8)**-8 = 1.07374182E9
(((8^8)**/8 = 1.34217728E8
(((8^8)*/8)+8 = 1.6777224E7
(((8^8)*/8)-8 = 1.6777208E7
(((8^8)*/8)*8 = 1.34217728E8
(((8^8)*/8)/8 = 2097152.0
(((8^8)/8)+8)+8 = 2097168.0
(((8^8)/8)+8)-8 = 2097152.0
(((8^8)/8)+8)*8 = 1.677728E7
(((8^8)/8)+8)/8 = 262145.0
(((8^8)/8)-8)+8 = 2097152.0
(((8^8)/8)-8)-8 = 2097136.0
(((8^8)/8)-8)*8 = 1.6777152E7
(((8^8)/8)-8)/8 = 262143.0
(((8^8)/8)*+8 = 1.6777224E7
(((8^8)/8)*-8 = 1.6777208E7
(((8^8)/8)**8 = 1.34217728E8
(((8^8)/8)*/8 = 2097152.0
(((8^8)/8)/8)+8 = 262152.0
(((8^8)/8)/8)-8 = 262136.0
(((8^8)/8)/8)*8 = 2097152.0
(((8^8)/8)/8)/8 = 32768.0

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Edit: big numbers are as big as floats will allow. I do not know how floats behave when overflowing.

Also, technically you could use the minus sign as a negation, and not subtraction

No solutions: 3,5,12,13,14 (On the off chance i missed something, please correct me )

Edit 3:
Apparently i cant use RPN to genarate a list of all possible combinations... that sucks )

#### _iPhoenix_

#2
Amazing. Perhaps check "Don't use smileys? as 8) turned into

3:
Spoiler
8/8+(8+8)/8
[close]
5:
Spoiler
8-(8+8+8)/8
[close]
12:
Spoiler
8+8*8/(8+8)
[close]
14:
Spoiler
8+8-(8+8)/8
[close]
Credits to PT_ ^^
And the longest continuous string of numbers that can be produced using this method is:
Spoiler
13: 0-12, but you could do negatives.
[close]

I got another one, and it's even more tedious.

If you have 4 of the numbers 1 - 9 (excluding 4, that makes this pointless), and you can only use one of the same type per equation, what numbers can you NOT express using only:
`(), +, - (or negative), /, ^, sqrt(), nth-root(), and factorial`.
1-200 is required, but -500 to 500 for brownie points! (yay)

I tested this out, and it is rather cool.

PLEASE USE A PROGRAM (any language is fine). DO NOT WASTE YOUR LIFE

• Calculators owned: Two TI-84+ CE's

"walruses are better than tuxedo chickens, all hail the great " ~ me
Evolution of my avatar:

#### Yuki

#3
I know it's not allowed but for the five 8's problem, if you use natural logarithms and cube roots...

...
ln(ln(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(8)))))))/ln(8))/ln(8+8/8)=-3
ln(ln(cuberoot(cuberoot(cuberoot(cuberoot(8)))))/ln(8))/ln(8+8/8)=-2
ln(ln(cuberoot(cuberoot(8)))/ln(8))/ln(8+8/8)=-1
ln(ln(8)/ln(8))/ln(8+8/8)=0
-ln(ln(cuberoot(cuberoot(8)))/ln(8))/ln(8+8/8)=1
-ln(ln(cuberoot(cuberoot(cuberoot(cuberoot(8)))))/ln(8))/ln(8+8/8)=2
-ln(ln(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(8)))))))/ln(8))/ln(8+8/8)=3
...

pretty print! But it include 3's

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and so on. Just add a cube root for every 1/2 and there you go, every integer ever.

`-ln(ln(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(cuberoot(8)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))/ln(8))/ln(8+8/8)=the answer to life, the universe and everything`
[close]
[close]
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#### _iPhoenix_

I might not disqualify you; that's pretty clever.
*disqualifies juju*
oops...

Meh. Your images aren't working for me, btw. Perhaps also find a super cheaty way to solve my second problem?
• Calculators owned: Two TI-84+ CE's

"walruses are better than tuxedo chickens, all hail the great " ~ me
Evolution of my avatar:

#### PT_

Here are the answers of your first question, I've checked every number <= 50, and the ones that are not in this list, are impossible to solve:

Spoiler
1:  (8-8)*8+8/8
2:  (8+8)/(8*8/8)
3:  8/8+(8+8)/8
4:  (8+8+8+8)/8
5:  8-(8+8+8)/8
6:  (8*8-8-8)/8
7:  8*8/8-8/8
8:  8*8*8/8/8
9:  8*8/8+8/8
10: (8*8+8+8)/8
11: 8+(8+8+8)/8
12: 8+8*8/(8+8)

14: 8+8-(8+8)/8
15: 8+8-(8/8)^8
16: (8*8)/((8+8)/8)
17: 8+8+(8/8)^8
18: 8+8+(8+8)/8

23: 8+8+8-8/8
24: 8+8+8+8-8
25: 8+8+8+8/8

32: (8+8)*(8+8)/8

40: 8+8+8+8+8

48: 8*(8-8/8)-8
[close]