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# Treebeard's Stumper Answer14 Feb 97

Here's a fun number cruncher for vacation week. Use just the four digits 1, 9, 9, 7 in that order, with parentheses and any standard math operations, to make all the numbers 0, 1, 2, ... For starters,

```    0  =   1*(9-9)*7
1  =   1^(997)              (to the power of)
2  =   1+sqrt(9)-(9-7)      (square root)
3  =   19-9-7
```

How far can you get? And what's the biggest number you can make?

The vacation challenge was to make numbers by adding math operations to the digits 1, 9, 9, and 7 in that order. With help from the group at rec.puzzles on the Internet, I managed to get all the numbers to 100.

It's useful that the square root of 9 is 3, and 3! is 6. (3! is "3 factorial," 1x2x3 = 6. There is usually a "!" key on calculators.)

The complete list is below. I can't get 92-94 without combining digits. Is 1997 exceptional?

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

10 = -1+9+9-7
11 = 1*9+9-7
12 = 1+9+9-7
13 = 1-9+sqrt(9)*7
14 = (1+9/9)*7
15 = -1^9+9+7
16 = (-1+9)*(9-7)
17 = -1+9*(9-7)
18 = 1*9*(9-7)
19 = 1+9*(9-7)

20 = (1+9)*(9-7)
21 = 1^9*sqrt(9)*7
22 = 1^9+sqrt(9)*7
23 = (1+9)*sqrt(9)-7
24 = -1+9+9+7
25 = 1*9+9+7
26 = 1+9+9+7
27 = 1*(sqrt(9))!+sqrt(9)*7
28 = (1+9/sqrt(9))*7
29 = -1+9+sqrt(9)*7

30 = 1*9+sqrt(9)*7
31 = 1+9+sqrt(9)*7
32 = (-1+9)*(-sqrt(9)+7)
33 = -1+sqrt(9)^sqrt(9)+7
34 = 1*sqrt(9)^sqrt(9)+7
35 = (-1+sqrt(9)+sqrt(9))*7
36 = 1*9*(-sqrt(9)+7)
37 = (1+9)*sqrt(9)+7
38 = (-1+(sqrt(9))!)*9-7
39 = 1*sqrt(9)*((sqrt(9))!+7)

40 = 1+sqrt(9)*((sqrt(9))!+7)
41 = -1^9+(sqrt(9))!*7
42 = 1*(sqrt(9)+sqrt(9))*7
43 = 1+(sqrt(9)+sqrt(9))*7
44 = 1+(sqrt(9))!*(sqrt(9))!+7
45 = 1*sqrt(9)+(sqrt(9))!*7
46 = 1+sqrt(9)+(sqrt(9))!*7
47 = -1+sqrt(9)*(9+7)
48 = 1*sqrt(9)*(9+7)
49 = (1-sqrt(9)+9)*7

50 = (-1+(sqrt(9))!)*(sqrt(9)+7)
51 = 1*9+(sqrt(9))!*7
52 = (-1+(sqrt(9))!)*9+7
53 = -1-9+9*7
54 = -1*9+9*7
55 = 1-9+9*7
56 = (-1+sqrt(9)*sqrt(9))*7
57 = -1*(sqrt(9))!+9*7
58 = 1-(sqrt(9))!+9*7
59 = -1-sqrt(9)+9*7

60 = -1*sqrt(9)+9*7
61 = 1-sqrt(9)+9*7
62 = -1^9+9*7
63 = 1^9*9*7
64 = 1^9+9*7
65 = -1+sqrt(9)+9*7
66 = 1*sqrt(9)+9*7
67 = 1+sqrt(9)+9*7
68 = -1+(sqrt(9))!+9*7
69 = 1*(sqrt(9))!+9*7

70 = (1^9+9)*7
71 = -1+9+9*7
72 = 1*9+9*7
73 = -1+9*9-7
74 = 1*9*9-7
75 = 1+9*9-7
76 = 1+sqrt(9)+9!/7!
77 = (-1+sqrt(9)+9)*7
78 = 1*(sqrt(9))!*((sqrt(9))!+7)
79 = (-1+9)*9+7

80 = -1+9+9!/7!
81 = 1*9+9!/7!
82 = 1+9+9!/7!
83 = (1+9)*9-7
84 = (1*sqrt(9)+9)*7
85 = 1+(sqrt(9)+9)*7
86 = -1+((sqrt(9))!)!/9+7
87 = -1+9*9+7
88 = 1*9*9+7
89 = 1+9*9+7

90 = 1*9*(sqrt(9)+7)
91 = 1+9*(sqrt(9)+7)
92 = 1*99-7
93 = 1+99-7
94 = -1*sqrt(9)+97
95 = -1+(sqrt(9))!*(9+7)
96 = 1*(sqrt(9))!*(9+7)
97 = (1+9)*9+7
98 = (-1+9+(sqrt(9))!)*7
99 = (-1+(sqrt(9))!)!-sqrt(9)*7

100 = (1+9)^(9-7)

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