Final answer:
The question is about calculating the mean number of lines a randomly tossed needle will cross on a grid, a probability problem known as Buffon's needle. Without the specific method or formula to apply to this case, we cannot determine the answer.
Step-by-step explanation:
The question concerns a classic problem in probability known as Buffon's needle problem, where we analyze the probability of a needle crossing lines on a grid when tossed at random. Since the length of the needle (21) and the spacing of the lines (1 unit apart) are specified, there is a well-established means to calculate the mean number of lines the needle will cross.
However, the method of calculation for this specific question is not outlined in the information provided; thus, the answer necessitates additional details regarding the arrangement and orientation of the needle relative to the lines.
Generally, when calculating the mean number of lines crossed, geometry and calculus are involved, taking into account both the length of the needle and the probability distribution for the angle at which the needle lands in relation to the grid lines. Without the specific formula or method, we cannot provide a numerical answer for the mean number of lines a needle of length 21 will cross.