$1\mathrm{.}3$ You have been assigned the task of computing the sum of $1,000$ four$-$digit

numbers as rapidly as possible. You hold in your hands a stack of $1,000$

index cards, each containing a single number, and you are in charge of

$1,000$ expert accountants, each with a calculator. You may choose to use

the services of any number of these accountants. The accountants are

sitting at desks in a cavernous room. The desks are organized into

$25$ rows and $40$ columns. Each accountant is able to pass cards to the four

accountants nearest her$-$in front, in back, to her left, and to her

right.

a$.$ Describe a fast method of distributing cards to accountants.

b$.$ Describe a fast method of accumulating the subtotals generated by the

active accountants into a grand total.

c$.$ Draw a graph that plots your best estimate of the time needed to

compute the grand total as a function of the number of accountants

you choose to use.

d$.$ Add another curve to the graph you drew in part c$,$ estimating the time

needed to compute the grand total of $10,000$ numbers, given

$1,$dots,$1,000$ accountants.

e$.$ Explain why $1,000$ accountants cannot perform the task $1,000$ times

faster than one accountant.