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A variation on the four fours puzzle: 2,0,0,8

A variation on the four fours puzzle: 2,0,0,8

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A
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For you arithmeticians out there the premise is simple:
Using only the numbers that make up this year: 2,0,0,8 (and all of them once) you must try and construct all the numbers between 0 and 100 (or beyond!)
You may use the following:
- parentheses
- addition
- subtraction
- multiplication
- division
- concatenation (ie: 02 or 80)
- exponentiation (you may use the minus sign for reciprocals)
- factorials (not sub-factorial)
- decimals finite or recurring (1/5 and 2/9 can be represented as .2 and .2bar respectively)
- square root (ie: sqrt(2) )

Here are a few to get you started:

0 = 0*(0 + 2 + 8)
1 = (0 + 2 + 8)^0
2 = 2 + 0*(0 + 8)
3 = 2 + 8^0 + 0
4 = 8/2 + 0 + 0
5 = .2^(-(0!)) + 0*8
6 = 8 - 2 + 0 + 0
7 = 8 - 2^0 + 0
8 = ?

yelrambob

Brooklyn

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8=8-0!-0!+2
9=8-0!+0+2
10=8+0+0+2
11=8+0!+0+2
12=8+0!+0!+2
13=8*2-0!+0

T
Kupikupopo!

Out of my mind

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Originally posted by Agerg
For you arithmeticians out there the premise is simple:
Using only the numbers that make up this year: 2,0,0,8 (and all of them once) you must try and construct all the numbers between 0 and 100 (or beyond!)
You may use the following:
- parentheses
- addition
- subtraction
- multiplication
- division
- concatenation (ie: 02 or 80)
- exponentiation (yo ...[text shortened]... = 2 + 8^0 + 0
4 = 8/2 + 0 + 0
5 = .2^(-(0!)) + 0*8
6 = 8 - 2 + 0 + 0
7 = 8 - 2^0 + 0
8 = ?
So you can only use a minus sign in a substraction and in a power?

A
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Originally posted by TheMaster37
So you can only use a minus sign in a substraction and in a power?
you can use it to represent negative numbers if you wish...how else would you care to use it (without adding more operations than is given?)

t

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14 = 8x2-0!-0!
15 = 8x2-0!-0
16 = 8x2-0+0
17 = 8x2+0+0!
18 = 8x2+0!+0!
19 = 20-(8x0)!
20 = 20-(8x0)
21 = 20+(8x0)!
22 = (2 catanation 0!)+(8x0)!
23 = (2+0!)x8-0!
24 = (2+0!)x8-0
25 = (2+0)!x8+0!
26 = 2 catanation (8-0!-0!)
27 = 2 catanation (8-0!-0)
28 = 2 catanation (8-0+0)
29 = 2 catanation (8+0!+0)
30 = 2 catanation (8+0!+0!)

p
Iron Pillar

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Originally posted by twilight2007
30 = 2 catanation (8+0!+0!)
......2 catanation (8+0!+0!)
=2 catanation (8+1+1)
=2 catanation 10
=210

A
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Originally posted by twilight2007
14 = 8x2-0!-0!
15 = 8x2-0!-0
16 = 8x2-0+0
17 = 8x2+0+0!
18 = 8x2+0!+0!
19 = 20-(8x0)!
20 = 20-(8x0)
21 = 20+(8x0)!
22 = (2 catanation 0!)+(8x0)!
23 = (2+0!)x8-0!
24 = (2+0!)x8-0
25 = (2+0)!x8+0!
26 = 2 catanation (8-0!-0!)
27 = 2 catanation (8-0!-0)
28 = 2 catanation (8-0+0)
29 = 2 catanation (8+0!+0)
30 = 2 catanation (8+0!+0!)
Unfortunately you cannot concatenate in the way you have demonstrated above.
Valid would be 20 + 08 or 28 + 0! + 0!
Invalid would be 8 concatenated with ((2 + 0!)! - 0!) or any other variations of this theme.
to write such numbers without the word "concatenate" would either render the end result meaningless or give a number different to what you intended.

t

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I see. So these would work then, right?

26 = 28-0!-0!
27 = 28-0!-0
28 = 28-0+0
29 = 28+0!+0
30 = 28+0!+0!

A
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aye 🙂

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