Using all possible arithmetic operations (addition, subtraction, multiplication,
division, exponents), and only the number 2, how many numbers beginning
with 1 can you write using only these restrictions.
I'll even get you started: 1 = 2/2; 15 = 2 + 2 + 2+ 2+ 2+ 2+ 2+ + 2/2
Challenge/Extension: How many ways can each number be written using only
these restrictions? For example is there more than one way to write 1 using
only the operations and 2s? What about 15? What about all of them?