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

Agerg
Posers and Puzzles 29 Jan '08 01:18
1. Agerg
The 'edit'or
29 Jan '08 01:181 edit
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 = ?
2. 29 Jan '08 03:07
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
3. TheMaster37
Kupikupopo!
29 Jan '08 09:19
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?
4. Agerg
The 'edit'or
29 Jan '08 10:422 edits
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?)
5. 02 Feb '08 20:18
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!)
6. 03 Feb '08 01:44
Originally posted by twilight2007
30 = 2 catanation (8+0!+0!)
......2 catanation (8+0!+0!)
=2 catanation (8+1+1)
=2 catanation 10
=210
7. Agerg
The 'edit'or
03 Feb '08 02:332 edits
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.
8. 03 Feb '08 22:012 edits
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!
9. Agerg
The 'edit'or
03 Feb '08 23:50
aye ðŸ™‚