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Treebeard's Stumper Answer
13 Feb 98

Crunching 1998

Here's an update of last year's vacation challenge. Use just the four digits 1, 9, 9, 8 in that order, with parentheses and any standard math operations, to make all the numbers 1 to 100. For starters,

1 = 1+(9-9)*8(* is times)
2 = (1^9)+9-8(^ is the power of)
3 = -1+sqrt(9)+(9-8)(square root)
4 = -1+sqrt(9)!-(9-8)(factorial, 3!=1x2x3=6)

Last year, we managed to get all the numbers using the digits of 1997. I'm sure this will not be possible in 2000. How far can we get this year?


The vacation challenge was to make numbers by adding math operations to the digits 1, 9, 9, 8 in that order. Kids in all grades at Dunn Middle School attacked this stumper before vacation, and we did it! Our impressive results are below. Next year, we'll find out if we can do 1999. I'm sure it's not possible for the year 2000. There's just not enough digits to work with. (It helps that 0!=1. Check your calculator, and don't ask me why!) I'm curious when is the next year after 2000 when it can be done?

Here is the complete list 0 to 100, as mostly found by the kids. Remember order of operations: PEMDAS -- parentheses, exponents, multiply and divide, then add and subtract. It's useful that the square root of 9 is 3, and 3! is 1*2*3=6. 3! is "3 factorial", all the integers up to 3 multiplied together. There's usually a "!" key on calculators. (We've been calling it "3 bang" at school.) 59 and 83 are extra tricky. (Sqrt(9)!)! = (3!)! = 6! = 720, and 720/8 = 90. Yahoo!


0=1*(9-9)*8
1=1+(9-9)*8
2=1*sqrt(9)-9+8
3=1+sqrt(9)-9+8
4=1*sqrt(9)+9-8
5=1+sqrt(9)+9-8
6=-1-9/9+8
7=-1+9-9+8
8=1*9/9+8
9=1+9-9+8


10=1*9+9-8
11=1+9+9-8
12=1+9/sqrt(9)+8
13=-1-sqrt(9)+9+8
14=-1*sqrt(9)+9+8
15=1-sqrt(9)+9+8
16=-1+sqrt(9)*sqrt(9)+8
17=1*sqrt(9)*sqrt(9)+8
18=1^9+9+8
19=1*sqrt(9)*9-8


20=1+sqrt(9)*9-8
21=1+sqrt(9)+9+8
22=1-sqrt(9)+sqrt(9)*8
23=1*9+sqrt(9)!+8
24=1+9+sqrt(9)!+8
25=-1+9+9+8
26=1*9+9+8
27=1+9+9+8
28=1+sqrt(9)+sqrt(9)*8
29=-1+sqrt(9)!+sqrt(9)*8


30=1*sqrt(9)!+sqrt(9)*8
31=1+sqrt(9)!+sqrt(9)*8
32=((1+sqrt(9))!/sqrt(9)!)*8
33=1*9+sqrt(9)*8
34=-1+sqrt(9)*9+8
35=1*sqrt(9)*9+8
36=1+sqrt(9)*9+8
37=(-1+sqrt(9)!)*9-8
38=-1-9+sqrt(9)!*8
39=-1*9+sqrt(9)!*8


40=(-1+sqrt(9)+sqrt(9))*8
41=(1+sqrt(9))!+9+8
42=-1*sqrt(9)!+sqrt(9)!*8
43=-1+sqrt(9)!*sqrt(9)!+8
44=1*sqrt(9)!*sqrt(9)!+8
45=1+sqrt(9)!*sqrt(9)!+8
46=1*sqrt(9)!*9-8
47=-1+(sqrt(9)+sqrt(9))*8
48=1*(sqrt(9)+sqrt(9))*8
49=1+(sqrt(9)+sqrt(9))*8


50=(1+sqrt(9)!)*sqrt(9)!+8
51=1*sqrt(9)*(9+8)
52=(1+9)*sqrt(9)!-8
53=(-1+sqrt(9)!)*9+8
54=1*sqrt(9)!+sqrt(9)!*8
55=1+sqrt(9)!+sqrt(9)!*8
56=(1+sqrt(9)+sqrt(9))*8
57=1*9+sqrt(9)!*8
58=1+9+sqrt(9)!*8
59=-1+sqrt(9)!/(.9-.8)


60=1*sqrt(9)!/(.9-.8)
61=-1+sqrt(9)!*9+8
62=-1-9+9*8
63=-1*9+9*8
64=1-9+9*8
65=-1-sqrt(9)!+9*8
66=-1*sqrt(9)!+9*8
67=1-sqrt(9)!+9*8
68=-1-sqrt(9)+9*8
69=-1*sqrt(9)+9*8


70=1-sqrt(9)+9*8
71=(1+sqrt(9)!)*9+8
72=1*sqrt(9)*sqrt(9)*8
73=1*9*9-8
74=1+9*9-8
75=1*sqrt(9)+9*8
76=1+sqrt(9)+9*8
77=-1+sqrt(9)!+9*8
78=1*sqrt(9)!+9*8
79=1+sqrt(9)!+9*8


80=-1+9+9*8
81=1*9+9*8
82=1+9+9*8
83=-1-sqrt(9)!+(sqrt(9)!)!/8
84=-1*sqrt(9)!+(sqrt(9)!)!/8
85=(-1+sqrt(9)!)*(9+8)
86=-1-sqrt(9)+(sqrt(9)!)!/8
87=-1*sqrt(9)+(sqrt(9)!)!/8
88=-1+9*9+8
89=1*9*9+8


90=1+9*9+8
91=(-1+9^sqrt(9))/8
92=-1+sqrt(9)+(sqrt(9)!)!/8
93=1*sqrt(9)+(sqrt(9)!)!/8
94=1+sqrt(9)+(sqrt(9)!)!/8
95=-1+(9+sqrt(9))*8
96=1*(9+sqrt(9))*8
97=1+(9+sqrt(9))*8
98=(1+9)*9+8
99=1*9*(sqrt(9)+8)


100=1+9*(sqrt(9)+8)

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Copyright © 1998 by Marc Kummel / mkummel@rain.org