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) )

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?

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.