A broken calculator can double any number or permute its digits (but 0 cannot go up front). Can we start with number 1 and obtain 78 by a series of these operations

it's impossible to obtain 78

Step-by-step explanation: Since the calculator can double any number or permute its digits except 0 

starting with number 1 

1, 2, 4, 8, 16, 32, 64, 128

Therefore, it's impossible to obtain 78 by a series of these operations

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2  

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation: