2019

2019

Making the integers from 0-99 using the digits (2, 0, 1, 9) and various
mathematical operators, including the binary operators:
- addition
- subtraction
- multiplication
- division
- exponentiation

the unary operators:
- factorial
- square root
- negation

The concatenation operator is also allowed, eg to make "90" from 9 and 0. It can
be applied to other non-atomic expressions, as in
35  = sqrt(9) || ((2 + 1)! - 0!)
but this isn't very pretty.

This can be extended to also allow unconcatenation - eg
73  = (sqrt(9)!)! @@ 0 + 2 - 1

In really desperatee times I may also be persuaded to allow string reversal, eg
76 = ~(201 / sqrt(9))

If you think it will be of any great use to you, feel free to use bitwise
operators like AND, OR, XOR.

You get bonus points for using the digits in the right order (ie an in-order
traversal of the leaf nodes of a parse tree of the expression returns 2019).

The columns are: initials of finder, "is it pretty?", "does it use nested
concatentation?", target number, "are the digits in-order?", solution.

Some rows are repeated because I like multiple solutions.

Really this whole thing is a bit of an exercise in seeing how far you can get
with as few operations as possible.  Currently, the important targets are
- find in-order solutions for
  14,15,16,21,25,26
- find non-concatenating solutions for
  34,35,94,95,97,98

ivd    0* = 2 * 0 * 1 * 9
ivd    1* = 2 * 0 + 1 ^ 9
ivd    2* = 2 + 0 * 1 * 9
ivd    3* = 2 * 0 * 1 + sqrt(9)
ivd    4* = 2 * 0 + 1 + sqrt(9)
ivd    5* = 2 + 0 * 1 + sqrt(9)
ivd    6* = 2 + 0 + 1 + sqrt(9)
ivd    7* = -2 + 0 * 1 + 9
ivd    8* = 2 * 0 - 1 + 9
ivd    9* = 2 * 0 * 1 + 9
ivd   10* = 2 * 0 + 1 + 9
ivd   11* = 2 + 0 * 1 + 9
ivd   12* = 2 + 0 + 1 + 9
ivd   13* = 2 + 0! + 1 + 9
ivd p 14  = 12 + sqrt(9) - 0!
ivd p 15  = 12 + sqrt(9) + 0
ivd p 16  = 12 + sqrt(9) + 0!
ivd   17* = -2 + 0 + 19
ivd   18* = -2 + 0! + 19
ivd   19* = -2 * 0 + 19
ivd   20* = 20 * 1 ^ 9
ivd   21  = 21 + 0 * 9
ivd   22* = 2 + 0! + 19
ivd   23* = 20 + 1 * sqrt(9)
ivd   24* = 20 + 1 + sqrt(9)
ivd   25  = (sqrt(9) + 1 + 0!) ^ 2
ivd   26  = 2 * (10 + sqrt(9))
ivd   27* = (2 + 0 + 1) ^ sqrt(9)
ivd   28* = 20 - 1 + 9
ivd   29* = 20 + 1 * 9
ivd   30* = 20 + 1 + 9
ivd   31  = 29 + 0! + 1
ivd   32  = (10 + sqrt(9)!) * 2
ivd   33  = (12 - 0!) * sqrt(9)
ivd  c34  = sqrt(9) || (2 + 0! + 1)
ivd  c35  = sqrt(9) || ((2 + 1)! - 0!)
ivd   36* = (2 + 0! + 1) * 9
ivd   37  = 2 * 19 - 0!
ivd   38* = 2 * (0 + 19)
ivd   39* = 20 + 19
ivd p 40* = 20 * (-1 + sqrt(9))
ivd p   * = 2 * (0! + 19)
ivd  c41  = (sqrt(9) + 2 - 1) || 0!
ivd   42  = 21 * (sqrt(9) - 0!)
ivd  c43  = (sqrt(9) + 1) || (0! + 2)
svd  c44  = (sqrt(9)! - 2) * (0! || 1)
ivd   45* = ((2 + 0!)! - 1) * 9
svd  c46  = (2 || sqrt(9)) * (1 + 0!)
svd p 47  = 2 * (0! + sqrt(9))! - 1
ivd   48  = 12 * (sqrt(9) + 0!)
ivd   49  = (9 - 0! - 1) ^ 2
ivd   50  = 10 * (sqrt(9) + 2)
svd  c51  = ((sqrt(9) + 2) || 0)  + 1
svd  c52  = ((sqrt(9) + 2) || 1) + 0!
ivd   53  = (2 + 1)! * 9 - 0!
ivd   54* = (2 + 0 + 1)! * 9
ivd   55  = (2 + 1)! * 9 + 0!
svd  c56* = ((2 + 0!)! - 1) || sqrt(9)!
ivd   57* = (2 + 0!) * 19
ivd   58  = 29 * (0! + 1)
svd  c59  = (sqrt(9)! || 1) - 2 + 0
ivd   60* = 20 * 1 * sqrt(9)
svd  c61  = (sqrt(9)! || 2) - 1 + 0
svd  c62  = (sqrt(9)! || 2) - 1 + 0!
ivd       = 2 ^ (sqrt(9)!) - 0! - 1
ivd   63* = ((2 + 0!)! + 1) * 9
ivd   64  = (9 - 1) ^ 2 + 0
ivd   65  = (9 - 1) ^ 2 + 0!
ivd   66  = (21 + 0!) * sqrt(9)
ivd p 67* = 201 / sqrt(9)
svd  c68* = (2 + 0!)! || (-1 + 9)
ivd  c69* = (2 + 0 + 1)! || 9
ivd p 70  = 210 / sqrt(9)
svd p 71  = 9^2 - 10
    p     = 91 - 20
lge p 72* = (2 + 0! + 1)! * sqrt(9)
svd  c73* = ((2 + 0!)! + 1) || sqrt(9)
svd p 73  = sqrt(9)! * 12 + 0!
svd   74  = (sqrt(9)!)! / 10 + 2
svd p 75  = 90 / 1.2
svd  c76* = ((2 + 0!)! + 1) || sqrt(9)!
          = 19 * (0! << 2)
ivd pc77  = (1 || 0!) * (9 - 2)
svd p 78  = sqrt(9)! * (12 + 0!)
svd  c78  = ((9 - 1) || 0) - 2
ivd   79  = 9 ^ 2 - 0! - 1
ivd   80  = 9 ^ 2 + 0 - 1
ivd p     = 2 ^ sqrt(9) * 10
ivd   81  = 9 ^ 2 + 0 * 1
ivd   82  = 9 ^ 2 + 1 * 0!
ivd   83  = 9 ^ 2 + 1 + 0!
ivd p 84  = 90 - (1 + 2)!
ivd  c85  = ~(29 * (0! + 1))
svd p 85  = 91 - (0! + 2)!
ivd  c86  = (9 - 0!) || (1 + 2)!
ivd   87  = 90 - 1 - 2
ivd   88  = 90 - 2 * 1
ivd   89  = 90 - 2 + 1
ivd p 90  = 90 * 1 ^ 2
ivd   91  = 90 - 1 + 2
ivd   92  = 90 + 1 * 2
ivd   93  = 90 + 1 + 2
ivd  c94  = 9 || (1 + 0! + 2)
ivd  c95  = 9 || ((2 + 1)! - 0!)
ivd p 96  = 90 + (1 + 2)!
ivd p     = sqrt(9 * 2 ^ 10)
ivd  c97  = 9 || ((2 + 1)! + 0!)
ivd  c98  = 9 || (10 - 2)
ivd p 99  = (12 - 0!) * 9
ivd p     = 102 - sqrt(9)