This puzzle comes from the January/February issue of Technology Review:

How many integers from 1 to 100 can you form using the digits 2, 0, 0, and 7 exactly once each, the operators +, -, x, /, and exponentiation? We desire solutions containing the minimum number of operators, and among solutions having a given number of operators, those using the digits in order 2, 0, 0, and 7 are preferred. Parentheses may be used for grouping; they do not count as operators. A leading minus sign does count as an operator.

Here is the solution I submitted:

1	207 ^ 0
2	2 + 0 * 70
3	2 + 70 ^ 0
4	7 - 2 + 0 ^ 0
5	7 - 2 + 0 + 0
6	7 - 20 ^ 0
7*	2 * 0 + 0 + 7
8*	20 ^ 0 + 7
9*	2 + 0 + 0 + 7
10*	2 + 0 ^ 0 + 7

13	2 * 7 - 0 ^ 0
14*	(2 + 0 + 0) * 7
15	7 * 2 + 0 ^ 0
16*	2 * (0 ^ 0 + 7)

19	20 - 7 ^ 0
20*	20 + 0 * 7
21	20 + 7 ^ 0

26	27 - 0 ^ 0
27	27 + 0 + 0
28	27 + 0 ^ 0

48	7 ^ 2 - 0 ^ 0
49	7 ^ 2 + 0 + 0
50	70 - 20

68	70 - 2 + 0
69	70 - 2 ^ 0
70	70 + 2 * 0
71	70 + 2 ^ 0
72	72 + 0 + 0
73	72 + 0 ^ 0

90	20 + 70

Solutions marked with a star maintain the 2007 digit ordering.