countdown number problem Problem statement:

Use the digits in the year 2017 and the operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and !! (double factorial) along with grouping symbols, to write expressions for the counting numbers 1 through 100.

All four digits must be used in the expression. Only the digits 2, 0, 1, 7 may be used. Multi-digit numbers such as 20, 210, or .02 will be accepted this year. Note that 0.02, while equivalent to .02, would not be acceptable since only one 0 is available this year. The square function may NOT be used. Nor may the cube, raise to a fourth power, or any other function that raises a number to a specific power. For example, (1 + 7)^2 - 0! is an acceptable way to write 63, because ^ is an acceptable operation and it uses exactly the digits 1, 7, 2, and 0. But 7^2 + 2 + 1 + 0! is not an acceptable way to write 53, because "^2" is not an acceptable operation, and there are not two 2's available. Similarly, 2^3 + 7 - 1 - 0! would not be an acceptable way to write 13 since "^3" is not an acceptable operation. Multifactorials other than the double factorials may NOT be used. The integer function may NOT be used. Nor may the round, floor, ceiling, or truncate functions. Remember that 0! by definition is equal to 1. For this puzzle, we will accept the value 0^0=1. The four digits can be used in any order, but challenge yourself to use the digits in the order 2, 0, 1, 7. encourage solutions using only the single digit numbers 2, 0, 1, and 7 rather than double digits like .02 or 71.