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Posers and Puzzles

Posers and Puzzles

  1. Standard member Agerg
    The 'edit'or
    29 Jan '08 01:18 / 1 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. Standard member 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. Standard member Agerg
    The 'edit'or
    29 Jan '08 10:42 / 2 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. Standard member preachingforjesus
    Iron Pillar
    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. Standard member Agerg
    The 'edit'or
    03 Feb '08 02:33 / 2 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 22:01 / 2 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. Standard member Agerg
    The 'edit'or
    03 Feb '08 23:50
    aye